Globally conservative weak solutions for a class of two-component nonlinear dispersive wave equations beyond wave breaking

Authors: Zhou, Yonghui, Li, Xiaowan, Ji, Shuguan

Source: Journal of Differential Equations. 427:538-559

Subject Terms: Initial value problems for systems of nonlinear higher-order PDEs, wave breaking, two-component nonlinear dispersive wave equations, globally conservative solutions, Methods of ordinary differential equations applied to PDEs, Weak solutions to PDEs

File Description: application/xml

Access URL: https://zbmath.org/8017129
https://doi.org/10.1016/j.jde.2025.01.089

Compressible Navier–Stokes–Coriolis system in critical Besov spaces: Compressible Navier-Stokes-Coriolis system in critical Besov spaces

Authors: Mikihiro Fujii, Keiichi Watanabe

Source: Journal of Differential Equations. 428:747-795

Subject Terms: Compressible Navier-Stokes equations, long time solutions, Hydrology, hydrography, oceanography, Geophysical flows, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, General theory of rotating fluids, PDEs in connection with fluid mechanics, PDEs in connection with geophysics, Asymptotic expansions of solutions to PDEs, Strichartz estimates, Navier-Stokes-Coriolis system, Mathematics - Analysis of PDEs, critical Besov spaces, FOS: Mathematics, Weak solutions to PDEs, Analysis of PDEs (math.AP)

File Description: application/xml

Access URL: http://arxiv.org/abs/2411.02191

Multiplicity of weak solutions in double phase Kirchhoff elliptic problems with Neumann conditions

Authors: Ahmed, Ahmed, Elemine Vall, Mohamed Saad Bouh, Boulaaras, Salah^{Aff3, IDs13661025020435_cor1}

Source: Boundary Value Problems. 2025(1)

Three Weak Solutions of (α1(·),…,αN(·))-Laplacian-Schrödinger-Kirchhoff Systems

Authors: Ahmed, Ahmed, Elemine Vall, Mohamed Saad Bouh^{Aff2, IDs13324025011203_cor1}, Ahmedatt, Taghi

Source: Analysis and Mathematical Physics. 15(5)

Global Solvability of Two-Dimensional Stochastic Chemotaxis-Navier-Stokes System: Global solvability of two-dimensional stochastic chemotaxis-Navier-Stokes system

Authors: Xu, Fan, Liu, Bin

Source: East Asian Journal on Applied Mathematics. 15:242-267

Subject Terms: martingale solution, Quasilinear parabolic equations, Stochastic partial differential equations (aspects of stochastic analysis), Cell movement (chemotaxis, etc.), stochastic chemotaxis-Navier-Stokes system, mild solution, Initial-boundary value problems for second-order parabolic systems, PDEs with randomness, stochastic partial differential equations, Weak solutions to PDEs

File Description: application/xml

Access URL: https://zbmath.org/8010618
https://doi.org/10.4208/eajam.2023-114.050224

Local well-posedness for a higher order Boussinesq type equation

Authors: Zhong, Long, Li, Shenghao

Source: Discrete and Continuous Dynamical Systems - B. 30:3625-3645

Subject Terms: trilinear estimate, local well-posedness, sixth order Boussinesq equation, PDEs in connection with fluid mechanics, Weak solutions to PDEs, bilinear estimate, Initial value problems for nonlinear higher-order PDEs

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A system of continuity equations with nonlocal interactions of Morse type

Authors: Di Francesco, Marco, Iorio, Valeria

Source: Communications on Pure and Applied Analysis. 24:1381-1405

Subject Terms: Optimal transportation, Primary: 35D30, 35F55, 35Q70. Secondary: 35Q49, 49Q22, PDEs in connection with mechanics of particles and systems of particles, Wasserstein gradient flow, nonlocal interaction, Mathematics - Analysis of PDEs, Transport equations, deterministic particle approximation, Morse potential, multi-agent system, Nonlocal interaction, FOS: Mathematics, Initial value problems for systems of nonlinear first-order PDEs, Weak solutions to PDEs, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2406.18771
https://zbmath.org/8035389
https://doi.org/10.3934/cpaa.2025041

Nonlinear Liouville-type theorem for a differential inequality involving Dunkl-Baouendi-Grushin operator

Authors: Jleli, Mohamed, Samet, Bessem

Source: Discrete and Continuous Dynamical Systems - S. 18:426-443

Subject Terms: Dunkl Laplacian, Partial differential inequalities and systems of partial differential inequalities, Liouville-type theorem, semilinear inequalities, weak solution, Degenerate elliptic equations, Dunkl-Baouendi-Grushin operator, Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs, Weak solutions to PDEs

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Access URL: https://zbmath.org/7989341
https://doi.org/10.3934/dcdss.2024087

A nonnegative weak solution to the phase field crystal model with degenerate mobility

Authors: Luong, Toai, Wise, Steven M.

Source: Discrete and Continuous Dynamical Systems - B. 30:3288-3309

Subject Terms: positive solution, phase field crystal, energy inequality, weak solution, Initial-boundary value problems for higher-order parabolic equations, Weak solutions to PDEs, Degenerate parabolic equations, degenerate mobility

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WAN Discretization of PDEs: Best Approximation, Stabilization, and Essential Boundary Conditions: WAN discretization of PDEs: best approximation, stabilization, and essential boundary conditions

Authors: Silvia Bertoluzza, Erik Burman, Cuiyu He

Source: SIAM Journal on Scientific Computing. 46:C688-C715

Subject Terms: Cea's Lemma, pseudotime XNODE, Numerical optimization and variational techniques, Systems of nonlinear higher-order PDEs, Pseudo-time XNODE, Cea's lemma, Stability and convergence of numerical methods for boundary value problems involving PDEs, Error bounds for initial value and initial-boundary value problems involving PDEs, PDEs on manifolds, weak adversarial network, Numerical PDE, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Weak solutions to PDEs, Weak Adversarial Network, Artificial neural networks and deep learning

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Access URL: https://zbmath.org/7964724
https://doi.org/10.1137/23m1588196

Measure-valued solutions to a generalized Landau–Lifshitz–Bloch equation: Measure-valued solutions to a generalized Landau-Lifshitz-Bloch equation

Authors: Chahid Ayouch, Driss Meskine, Mouhcine Tilioua

Source: Zeitschrift für Analysis und ihre Anwendungen. 44:1-15

Subject Terms: Initial-boundary value problems for systems of nonlinear higher-order PDEs, Statistical mechanics of magnetic materials, Young measures, Existence problems for PDEs: global existence, local existence, non-existence, PDEs with measure, Weak solutions to PDEs, Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations, PDEs in connection with optics and electromagnetic theory, Landau-Lifshitz-Bloch equation, measure-valued solutions

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Access URL: https://zbmath.org/8021679
https://doi.org/10.4171/zaa/1783

Non-linear biphasic mixture model: Existence and uniqueness results: Non-linear biphasic mixture model: existence and uniqueness results

Authors: Meraj Alam, Adrian Muntean, Raja Sekhar G P

Source: European Journal of Applied Mathematics, Pp 1-25

Subject Terms: Matematik, fixed-point theory, 76Txx, 35D30, hydraulic resistivity, Multiphase and multicomponent flows, 01 natural sciences, in-vitro tumour, Mathematics - Analysis of PDEs, Biological fluid mechanics, 35Q74, weak solutions, QA1-939, biphasic mixture theory, FOS: Mathematics, 76Txx, 76Zxx (Primary) 35Q74, 35D30 (Secondary), 0101 mathematics, PDEs in connection with mechanics of deformable solids, Weak solutions to PDEs, 76Zxx, Mathematics, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2202.06059
https://zbmath.org/8035155
https://doi.org/10.1017/s0956792524000251
https://doaj.org/article/c292274aceb84b85ab03c6b26faf5c0f
http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-101885

Analysis and numerical simulation of a generalized compressible Cahn–Hilliard–Navier–Stokes model with friction effects: Analysis and numerical simulation of a generalized compressible Cahn-Hilliard-Navier-Stokes model with friction effects

Authors: Elbar, Charles, Poulain, Alexandre

Contributors: Sciences, EDP

Source: ESAIM: Mathematical Modelling and Numerical Analysis. 58:1989-2034

Subject Terms: Cell biology, Iterative numerical methods for linear systems, scalar auxiliary variable method, 35B40, 35B45, 35G20, 35Q35, 35Q92, 65M08, PDEs in connection with biology, chemistry and other natural sciences, Nonlinear higher-order PDEs, [MATH] Mathematics [math], PDEs in connection with fluid mechanics, Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics, Physiological flows, 01 natural sciences, Cahn-Hilliard equation, Navier-Stokes equation, numerical simulations, Fixed-point theorems, Mathematics - Analysis of PDEs, FOS: Mathematics, Cahn–Hilliard equation, Mathematics - Numerical Analysis, 0101 mathematics, Weak solutions to PDEs, Physiological flow, Navier–Stokes equation, Asymptotic behavior of solutions to PDEs, mathematical modeling, Existence problems for PDEs: global existence, local existence, non-existence, Numerical Analysis (math.NA), A priori estimates in context of PDEs, asymptotic analysis, Friction in solid mechanics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2305.05623
https://hal.science/hal-04747238v1
https://hal.science/hal-04747238v1/document
https://doi.org/10.1051/m2an/2024063

Global solvability in a three-dimensional self-consistent chemotaxis-Navier–Stokes system with porous medium diffusion: Global solvability in a three-dimensional self-consistent chemotaxis-Navier-Stokes system with porous medium diffusion

Authors: Chao Liu, Bin Liu

Source: Mathematical Models and Methods in Applied Sciences. 34:1825-1860

Subject Terms: self-consistent, Quasilinear parabolic equations, chemotaxis-Navier-Stokes system, porous medium diffusion, Cell movement (chemotaxis, etc.), weak solution, Initial-boundary value problems for second-order parabolic systems, 0101 mathematics, Weak solutions to PDEs, PDEs in connection with fluid mechanics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/7938956
https://doi.org/10.1142/s0218202524500374

Hölder Regularity of the Pressure for Weak Solutions of the 3D Euler Equations in Bounded Domains: Hölder regularity of the pressure for weak solutions of the 3D Euler equations in bounded domains

Authors: Bardos, C, Boutros, DW, Titi, ES

Contributors: DSpace at Cambridge pro (8.1)

Source: Archive for Rational Mechanics and Analysis. 249

Subject Terms: regularity, Smoothness and regularity of solutions to PDEs, 4901 Applied Mathematics, Analysis of PDEs, 4904 Pure Mathematics, weak solution, Euler equations, incompressible Euler equations, 35Q31 (primary), 35Q35, 76B03, 35J05, 35J08, 35J25, 35D30 (secondary), Existence, uniqueness, and regularity theory for incompressible inviscid fluids, FOS: Mathematics, 49 Mathematical Sciences, Weak solutions to PDEs, Analysis of PDEs (math.AP)

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2304.01952
https://zbmath.org/8029951
https://doi.org/10.1007/s00205-025-02090-3
https://www.repository.cam.ac.uk/handle/1810/379258
https://doi.org/10.1007/s00205-025-02090-3
https://doi.org/10.17863/cam.115410

On the Well-Posedness and Long Time Dynamics for a Coupled Nonlinear Bridge System with Past History: On the well-posedness and long time dynamics for a coupled nonlinear bridge system with past history

Authors: Soh Edwin Mukiawa, Salim A. Messaoudi

Source: Applied Mathematics & Optimization. 91

Subject Terms: well-posedness, Initial-boundary value problems for higher-order hyperbolic systems, Higher-order semilinear hyperbolic equations, past history, attractors, suspension bridge, Attractors, Weak solutions to PDEs, PDEs in connection with mechanics of deformable solids

File Description: application/xml

Access URL: https://zbmath.org/8028852
https://doi.org/10.1007/s00245-025-10252-8

Log‐BMO matrix weights and quasilinear elliptic equations with Orlicz growth in Reifenberg domains: Log-BMO matrix weights and quasilinear elliptic equations with Orlicz growth in Reifenberg domains

Authors: Byun, Sun-Sig, Yang, Rui

Source: Journal of the London Mathematical Society. 111

Subject Terms: Quasilinear elliptic equations, Smoothness and regularity of solutions to PDEs, Weak solutions to PDEs

File Description: application/xml

Access URL: https://zbmath.org/8037464
https://doi.org/10.1112/jlms.70151

On the Regularity of Time-Harmonic Maxwell Equations with Impedance Boundary Conditions: On the regularity of time-harmonic Maxwell equations with impedance boundary conditions

Authors: Chen, Zhiming

Source: Communications on Applied Mathematics and Computation. 7:759-770

Subject Terms: Maxwell equations, Smoothness and regularity of solutions to PDEs, impedance boundary condition, \(H^2\) regularity, Weak solutions to PDEs, PDEs in connection with optics and electromagnetic theory

File Description: application/xml

Access URL: https://zbmath.org/8034298
https://doi.org/10.1007/s42967-024-00386-x

Diffuse-interface approximation and weak–strong uniqueness of anisotropic mean curvature flow: Diffuse-interface approximation and weak-strong uniqueness of anisotropic mean curvature flow

Authors: Tim Laux, Kerrek Stinson, Clemens Ullrich

Source: European Journal of Applied Mathematics, Pp 1-61

Subject Terms: anisotropic mean curvature flow, weak-strong uniqueness, 35D30, weak–strong uniqueness, Flows related to mean curvature, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, sharp interface limit, 53E10, 35A02, 01 natural sciences, Mathematics - Analysis of PDEs, QA1-939, FOS: Mathematics, distributional solution, 35A02, 35D30, 53E30, 0101 mathematics, Weak solutions to PDEs, Mathematics, Analysis of PDEs (math.AP)

File Description: application/xml

Access URL: http://arxiv.org/abs/2212.11939
https://zbmath.org/8035153
https://doi.org/10.1017/s0956792524000226
https://doaj.org/article/dc3a2082db3c4af9ba0820e960f5a503

About Sobolev spaces on fractals: fractal gradians and Laplacians

Authors: Golmankhaneh, Alireza Khali, Jørgensen, Palle E. T., Serpa, Cristina, Welch, Kerri

Source: Aequationes mathematicae. 99:465-490

Subject Terms: Sobolev (and similar kinds of) spaces of functions on metric spaces, analysis on metric spaces, Fractals, fractal Laplace operator, fractal Lipschitz continuity, fractal Sobolev spaces, Differentiable functions on analytic spaces, differentiable spaces, \(L^p\)-spaces and other function spaces on groups, semigroups, etc, Hilbert spaces of continuous, differentiable or analytic functions, Weak solutions to PDEs, fractal weak derivative

File Description: application/xml

Access URL: https://zbmath.org/8032536
https://doi.org/10.1007/s00010-024-01060-6