Academic Journal
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
| Τίτλος: | 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 |
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| Συγγραφείς: | Sperone, Gianmarco |
| Πηγή: | Calculus of Variations and Partial Differential Equations. 62 |
| Στοιχεία εκδότη: | Springer Science and Business Media LLC, 2023. |
| Έτος έκδοσης: | 2023 |
| Θεματικοί όροι: | 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 |
| Περιγραφή: | This paper concerns the steady motion of a viscous incompressible fluid in an obstructed finite pipe, which is modeled through the Navier-Stokes equations with mixed boundary conditions involving the Bernoulli pressure and the tangential velocity on the inlet and outlet of the tube, while a transversal flux rate \(F\) is prescribed along the pipe. Existence of a weak solution to such Navier-Stokes system is proved without any restriction on the data by means of the Leray-Schauder principle, in which the required a priori estimate is obtained by a contradiction argument based on Bernoulli's law. Through variational techniques and with the use of an exact flux carrier, an explicit upper bound on \(F\) (in terms of the viscosity, diameter and length of the tube) ensuring the uniqueness of such weak solution is given. This upper bound is shown to converge to zero at a given rate as the length of the pipe goes to infinity. In an axially symmetric framework, the author also proves the existence of a weak solution displaying rotational symmetry. |
| Τύπος εγγράφου: | Article |
| Περιγραφή αρχείου: | application/xml; application/pdf |
| Γλώσσα: | English |
| ISSN: | 1432-0835 0944-2669 |
| DOI: | 10.1007/s00526-023-02578-4 |
| Rights: | Springer Nature TDM |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....d471e4d5146fca3f6f11b1f06be958b6 |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 14320835 09442669 |
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| DOI: | 10.1007/s00526-023-02578-4 |