The importance of Luis Caffarelli’s work in the study of fluids: The importance of Luis Caffarelli's work in the study of fluids

Authors: Esteban, Maria J.

Source: Bulletin of the American Mathematical Society. 62:301-325

Subject Terms: regularity, fluid mechanics, Navier-Stokes equations for incompressible viscous fluids, Wakes and jets, jet flows, boundary regularity, Mathematics - Analysis of PDEs, Primary 76D03, Secondary 76D05, 76B10, 76D25, 76D45, interface regularity free boundaries capillary drops, Capillarity (surface tension) for incompressible viscous fluids, FOS: Mathematics, Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing, Navier-Stokes equations, quasi-geostrophic models, Existence, uniqueness, and regularity theory for incompressible viscous fluids, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2503.02575

Global Fujita-Kato solutions to 3D inhomogeneous nematic liquid crystal flows with only bounded density allowing vacuum

Authors: Chen, Dongxiang, Liang, Xingyu, Chen, Xiaoli, Ye, Xia

Source: Communications on Pure and Applied Analysis. 24:1538-1565

Subject Terms: inhomogeneous nematic liquid crystal flows, global existence, critical Sobolev space, uniqueness, PDEs in connection with fluid mechanics, Stability in context of PDEs, Existence, uniqueness, and regularity theory for incompressible viscous fluids

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Access URL: https://zbmath.org/8035396
https://doi.org/10.3934/cpaa.2025048

On asymptotic stability of Couette flow for 2-D Boussinesq system in whole space via Green's function

Authors: Wang, Gaofeng, Wang, Lijuan

Source: Discrete and Continuous Dynamical Systems - B. 30:3014-3041

Subject Terms: Boussinesq system, Fundamental solutions, Green's function methods, etc. for initial value and initial-boundary value problems involving PDEs, Asymptotic behavior of solutions to PDEs, Perturbations in context of PDEs, stability threshold, Navier-Stokes equations, Green's function, PDEs in connection with fluid mechanics, Couette flow, Existence, uniqueness, and regularity theory for incompressible viscous fluids

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Global‐in‐time well‐posedness of solutions for the 2D hyperbolic Prandtl equations in an analytic framework: Global-in-time well-posedness of solutions for the 2D hyperbolic Prandtl equations in an analytic framework

Authors: Xiaolei Dong

Source: Mathematical Methods in the Applied Sciences. 48:3895-3906

Subject Terms: global existence, hyperbolic Prandtl equations, Boundary-layer theory for compressible fluids and gas dynamics, analytic space, uniqueness, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, PDEs in connection with fluid mechanics, Existence, uniqueness, and regularity theory for incompressible viscous fluids, Waves for incompressible viscous fluids

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Access URL: https://zbmath.org/8021990
https://doi.org/10.1002/mma.10523

Journal of Partial Differential Equations: Hölder Zygmund space techniques to the Navier-Stokes equations in the whole space

Authors: Chen, Zhi-Min, Zhao, Y., Yang, Y.

Subject Terms: local solutions, Regularity of generalized solutions of PDE, Holder Zygmund spaces, Navier-Stokes equations, Existence, uniqueness, and regularity theory for incompressible viscous fluids

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Access URL: https://zbmath.org/1474945
https://eprints.soton.ac.uk/204461/

Stability and Large-Time Behavior on 3D Incompressible MHD Equations with Partial Dissipation Near a Background Magnetic Field: Stability and large-time behavior on 3D incompressible MHD equations with partial dissipation near a background magnetic field

Authors: Hongxia Lin, Jiahong Wu, Yi Zhu

Source: Archive for Rational Mechanics and Analysis. 249

Subject Terms: Mathematics - Analysis of PDEs, FOS: Mathematics, 0101 mathematics, PDEs in connection with fluid mechanics, 35B35, Existence, uniqueness, and regularity theory for incompressible viscous fluids, 01 natural sciences, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2210.16600
https://zbmath.org/8029949
https://doi.org/10.1007/s00205-025-02100-4

Stability for the 2D Anisotropic Magnetohydrodynamic Equations with Only Horizontal Magnetic Diffusion: Stability for the 2D anisotropic magnetohydrodynamic equations with only horizontal magnetic diffusion

Authors: Lin, Hongxia, Suo, Xiaoxiao, Wu, Jiahong, Xu, Xiaojing

Source: Journal of Nonlinear Science. 35

Subject Terms: horizontal magnetic diffusion, background magnetic field, Magnetohydrodynamics and electrohydrodynamics, magnetohydrodynamic equation, stability, PDEs in connection with fluid mechanics, Existence, uniqueness, and regularity theory for incompressible viscous fluids

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Access URL: https://zbmath.org/8032057
https://doi.org/10.1007/s00332-025-10147-6

Gevrey Type Error Estimates of Solutions to the Navier–Stokes Equations: Gevrey type error estimates of solutions to the Navier-Stokes equations

Authors: Yuta Koizumi

Source: Journal of Mathematical Fluid Mechanics. 27

Subject Terms: Navier-Stokes equations, Existence, uniqueness, and regularity theory for incompressible viscous fluids

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Access URL: https://zbmath.org/8013099
https://doi.org/10.1007/s00021-025-00924-4

The regularity criteria of weak solutions to 3D axisymmetric incompressible Boussinesq equations

Authors: Dong, Yu, Huang, Yaofang, Li, Li, Lu, Qing

Source: Acta Mathematica Scientia. 43:2387-2397

Subject Terms: axisymmetry, Smoothness and regularity of solutions to PDEs, regularity criteria, PDEs in connection with fluid mechanics, Boussinesq equations, PDEs in connection with geophysics, Existence, uniqueness, and regularity theory for incompressible viscous fluids

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Gevrey Solutions of Quasi-Linear Hyperbolic Hydrostatic Navier–Stokes System: Gevrey solutions of quasi-linear hyperbolic hydrostatic Navier-Stokes system

Authors: Wei-Xi Li, Marius Paicu, Ping Zhang

Source: SIAM Journal on Mathematical Analysis. 55:6194-6228

Subject Terms: Gevrey class, Second-order quasilinear hyperbolic equations, well-posedness, PDEs on time scales, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, hyperbolic hydrostatic Navier-Stokes system, Navier-Stokes equations, Existence, uniqueness, and regularity theory for incompressible viscous fluids, quasi-linear system

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Partial boundary regularity for the Navier–Stokes equations in time-dependent domains: Partial boundary regularity for the Navier-Stokes equations in time-dependent domains

Authors: Dominic Breit

Source: Journal of Differential Equations. 434:113299

Subject Terms: Mathematics - Analysis of PDEs, Smoothness and regularity of solutions to PDEs, Navier-Stokes equations for incompressible viscous fluids, FOS: Mathematics, Navier-Stokes equations, PDEs in connection with mechanics of deformable solids, Existence, uniqueness, and regularity theory for incompressible viscous fluids, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2305.02602
https://zbmath.org/8034589
https://doi.org/10.1016/j.jde.2025.113299

Large Time Behavior for Solutions to the Anisotropic Navier–Stokes Equations in a 3D Half-space: Large time behavior for solutions to the anisotropic Navier-Stokes equations in a 3D half-space

Authors: Fujii, Mikihiro, Li, Yang

Source: International Mathematics Research Notices. 2025

Subject Terms: One-parameter semigroups and linear evolution equations, Littlewood-Paley analysis, Maximal functions, Littlewood-Paley theory, Asymptotic behavior of solutions to PDEs, Navier-Stokes equations for incompressible viscous fluids, 01 natural sciences, 35Q30, 35B40, 35Q35, Mathematics - Analysis of PDEs, 0103 physical sciences, FOS: Mathematics, Navier-Stokes equations, 0101 mathematics, Existence, uniqueness, and regularity theory for incompressible viscous fluids, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2410.04904

Global regularity for the 2D micropolar Rayleigh-B é nard convection system with velocity zero dissipation and temperature critical dissipation: Global regularity for the 2D micropolar Rayleigh-Bénard convection system with velocity zero dissipation and temperature fractional diffusion

Authors: Baoquan Yuan, Changhao Li

Source: Mathematical Methods in the Applied Sciences. 47:7502-7517

Subject Terms: micropolar Rayleigh-Bénard, global regularity, Mathematics - Analysis of PDEs, Smoothness and regularity of solutions to PDEs, 35Q35, 35B65, 76D03, FOS: Mathematics, PDEs in connection with fluid mechanics, Sobolev space, Existence, uniqueness, and regularity theory for incompressible viscous fluids, Besov space, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2307.06637
https://zbmath.org/8027789

Gevrey Well-Posedness of Quasi-Linear Hyperbolic Prandtl Equations: Gevrey well-posedness of quasi-linear hyperbolic Prandtl equations

Authors: Li, Wei-Xi, Yang, Tong, Zhang, Ping

Source: Communications in Mathematical Analysis and Applications. 2:388-420

Subject Terms: Gevrey class, hyperbolic Prandtl equations, Mathematics - Analysis of PDEs, Degenerate hyperbolic equations, Second-order quasilinear hyperbolic equations, quasi-linear, Boundary-layer theory, separation and reattachment, higher-order effects, Navier-Stokes equations, 0101 mathematics, Existence, uniqueness, and regularity theory for incompressible viscous fluids, 01 natural sciences

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Access URL: http://arxiv.org/abs/2401.11230
https://zbmath.org/7816840
https://doi.org/10.4208/cmaa.2023-0007

Quantitative aspects on the ill-posedness of the Prandtl and hyperbolic Prandtl equations

Authors: De Anna F., Kortum J., Scrobogna S.

Contributors: De Anna, F., Kortum, J., Scrobogna, S.

Source: Zeitschrift für angewandte Mathematik und Physik. 75

Subject Terms: Gevrey class, Growth rate, dispersion relation, Prandtl number, Dispersion, Boundary-layer theory, separation and reattachment, higher-order effects, Sobolev space, 01 natural sciences, Mathematics - Analysis of PDEs, Quantum theory, Sobolev spaces, 0103 physical sciences, FOS: Mathematics, Navier-Stokes equations, 0101 mathematics, linearised Prandtl equations, Dispersions, Existence, uniqueness, and regularity theory for incompressible viscous fluids, non-monotonic shear flow, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2305.04664
https://hdl.handle.net/11368/3073020
https://link.springer.com/article/10.1007/s00033-023-02179-3

3D Hyperbolic Navier-Stokes Equations in a Thin Strip: Global Well-Posedness and Hydrostatic Limit in Gevrey Space: 3D hyperbolic Navier-Stokes equations in a thin strip: global well-posedness and hydrostatic limit in Gevrey space

Authors: Li, Wei-Xi, Yang, Tong

Source: Communications in Mathematical Analysis and Applications. 1:471-502

Subject Terms: 3D hydrostatic Navier-Stokes equations, Gevrey class, Mathematics - Analysis of PDEs, hydrostatic limit, FOS: Mathematics, Navier-Stokes equations, Boundary-layer theory, separation and reattachment, higher-order effects, 0101 mathematics, Existence, uniqueness, and regularity theory for incompressible viscous fluids, global well-posedness, 01 natural sciences, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2204.09173
https://zbmath.org/7730361
https://doi.org/10.4208/cmaa.2022-0007

Gevrey Well-Posedness of the Hyperbolic Prandtl Equations: Gevrey well-posedness of the hyperbolic Prandtl equations

Authors: Li, Wei-Xi, Xu, Rui

Source: Communications in Mathematical Research. 38:605-624

Subject Terms: hyperbolic Prandtl boundary layer, Mathematics - Analysis of PDEs, well-posedness, FOS: Mathematics, Navier-Stokes equations, Boundary-layer theory, separation and reattachment, higher-order effects, Gervey space, 0101 mathematics, PDEs in connection with fluid mechanics, abstract Cauchy-Kowalewski theorem, Existence, uniqueness, and regularity theory for incompressible viscous fluids, 01 natural sciences, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2112.10450

Steady-state Navier–Stokes flow in an obstructed pipe under mixed boundary conditions and with a prescribed transversal flux rate: Steady-state Navier-Stokes flow in an obstructed pipe under mixed boundary conditions and with a prescribed transversal flux rate

Authors: Sperone, Gianmarco

Source: Calculus of Variations and Partial Differential Equations. 62

Subject Terms: weak solution existence, Bernoulli pressure, uniqueness, Navier-Stokes equations, Existence, uniqueness, and regularity theory for incompressible viscous fluids, variational method, Leray-Schauder principle, Sobolev embedding constant, Bogovskii constant

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On well-posedness of Navier–Stokes variational inequalities: On well-posedness of Navier-Stokes variational inequalities

Authors: Weimin Han, Yuan Yao

Source: APPLIED MATHEMATICS LETTERS

Subject Terms: well-posedness, Navier-Stokes equations for incompressible viscous fluids, Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, Navier-Stokes equations, Boundary-layer theory, separation and reattachment, higher-order effects, variational inequality, Existence, uniqueness, and regularity theory for incompressible viscous fluids

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Access URL: https://zbmath.org/7879169
https://doi.org/10.1016/j.aml.2024.109121

Global Well-Posedness for the Compressible Euler-Korteweg Equations with Damping In L2-Lp Critical Besov Space And Relaxation Limit: Global well-posedness for the compressible Euler-Korteweg equations with damping in \(L^2\)-\(L^p\) critical Besov space and relaxation limit

Authors: Zhang, Jianzhong, Cao, Hongmei

Subject Terms: \(L^2\)-\(L^p\) critical Besov spaces, Navier-Stokes equations, Euler-Korteweg equations with damping, Existence, uniqueness, and regularity theory for incompressible viscous fluids, global well-posedness, relaxation limit

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