Journal•ISSN: 1422-6928
Journal of Mathematical Fluid Mechanics
Birkhäuser
About: Journal of Mathematical Fluid Mechanics is an academic journal published by Birkhäuser. The journal publishes majorly in the area(s): Navier–Stokes equations & Boundary value problem. It has an ISSN identifier of 1422-6928. Over the lifetime, 1035 publications have been published receiving 16613 citations. The journal is also known as: JMFM.
Topics: Navier–Stokes equations, Boundary value problem, Uniqueness, Bounded function, Compressibility
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TL;DR: In this paper, the existence of globally defined weak solutions to the Navier-Stokes equations of compressible isentropic flows in 3D space dimensions was proved on the condition that the adiabatic constant satisfies γ ≥ 3/2.
Abstract: We prove the existence of globally defined weak solutions to the Navier—Stokes equations of compressible isentropic flows in three space dimensions on condition that the adiabatic constant satisfies
$ \gamma > 3/2 $
.
799 citations
TL;DR: In this paper, a criterion of local Holder continuity for suitable weak solutions to Navier-Stokes equations is presented. But the main part of the proof is based on a blow-up procedure and can be applied to other problems in spaces of solenoidal vector fields.
Abstract: We prove a criterion of local Holder continuity for suitable weak solutions to the Navier—Stokes equations. One of the main part of the proof, based on a blow-up procedure, has quite general nature and can be applied to other problems in spaces of solenoidal vector fields.
309 citations
TL;DR: In this article, the authors introduced the notion of relative entropy for the weak solutions to the compressible Navier-Stokes system and established the weak-strong uniqueness property in the class of finite energy weak solutions.
Abstract: We introduce the notion of relative entropy for the weak solutions to the compressible Navier–Stokes system. In particular, we show that any finite energy weak solution satisfies a relative entropy inequality with respect to any couple of smooth functions satisfying relevant boundary conditions. As a corollary, we establish the weak-strong uniqueness property in the class of finite energy weak solutions, extending thus the classical result of Prodi and Serrin to the class of compressible fluid flows.
267 citations
TL;DR: In this paper, the strong solvability of Navier-Stokes equations for rough initial data was studied and it was shown that there exists essentially only one maximal strong solution and various concepts of generalized solutions coincide.
Abstract: In this paper we study the strong solvability of the Navier—Stokes equations for rough initial data. We prove that there exists essentially only one maximal strong solution and that various concepts of generalized solutions coincide. We also apply our results to Leray—Hopf weak solutions to get improvements over some known uniqueness and smoothness theorems. We deal with rather general domains including, in particular, those having compact boundaries.
224 citations
TL;DR: In this paper, the existence of weak solutions for an unsteady fluid-structure interaction problem with a flexible elastic plate located on one part of the fluid boundary is studied.
Abstract: The purpose of this work is to study the existence of solutions for an unsteady fluid-structure interaction problem. We consider a three-dimensional viscous incompressible fluid governed by the Navier–Stokes equations, interacting with a flexible elastic plate located on one part of the fluid boundary. The fluid domain evolves according to the structure’s displacement, itself resulting from the fluid force. We prove the existence of at least one weak solution as long as the structure does not touch the fixed part of the fluid boundary. The same result holds also for a two-dimensional fluid interacting with a one-dimensional membrane.
214 citations