1,720,977 research outputs found
Some remark on the existence of infinitely many nonphysical solutions to the incompressible Navier-Stokes equations
Get PDFWe prove that there exist infinitely many distributional solutions with infinite kinetic energy to both the incompressible Navier-Stokes equations in and Burgers equation in with vanishing initial data
On the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids
Get PDFWe study a class of 2D solutions of a Bloch-Torrey regularization of the Rosensweig system in the whole space, which arise when the initial data and the external magnetic field are 2D. We prove that such solutions are globally defined if the initial data is in H^k\pare{\bR^2}, k\geqslant 1
Well-posedness of an asymptotic model for capillarity-driven free boundary Darcy flow in porous media in the critical Sobolev space
Get PDFWe prove that the quadratic approximation of the capillarity-driven free-boundary Darcy flow, derived in Granero-Belinchon and Scrobogna (2019), is well posed in (H)over dot(3/2) (S-1), and globally well-posed if the initial datum is small in (H)over dot(3/2) (S-1)
Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity
Get PDFWe prove that the three-dimensional, periodic primitive equations with zero vertical diffusivity are globally well posed if the Rossby and Froude number are sufficiently small. The initial data is considered to be of zero horizontal average and the space domain may be resonant. No smallness assumption is assumed on the initial data
Zero limit of entropic relaxation time for the Shliomis model of ferrofluids
Get PDFWe construct solutions for the Shilomis model of ferrofluids in a critical space, uniformly in the entropic relaxation time tau is an element of (0, tau(0)). This allows us to study the convergence when tau -> 0 for such solutions. (C) 2021 Elsevier Inc. All rights reserved
DERIVATION OF LIMIT EQUATIONS FOR A SINGULAR PERTURBATION OF A 3D PERIODIC BOUSSINESQ SYSTEM
No full textWe consider a system describing the long-time dynamics of an hydrodynamical, density-dependent flow under the effects of gravitational forces. We prove that if the Froude number is sufficiently small such system is globally well posed with respect to a H-s, s > 1/2 Sobolev regularity. Moreover if the Froude number converges to zero we prove that the solutions of the aforementioned system converge (strongly) to a stratified three-dimensional Navier-Stokes system. No smallness assumption is assumed on the initial data
Global existence and convergence of nondimensionalized incompressible Navier-Stokes equations in low Froude number regime
No full textWe prove that the incompressible, density dependent, Navier-Stokes equations are globally well posed in a low Froude number regime. The density profile is supposed to be increasing in depth and linearized around a stable state. Moreover if the Froude number tends to zero we prove that such system converges (strongly) to a two-dimensional, stratified Navier-Stokes equations with full diffusivity. No smallness assumption is considered on the initial data
Dispersive effects of weakly compressible and fast rotating inviscid fluids
Get PDFWe consider a system describing the motion of an isentropic, inviscid, weakly compressible, fast rotating fluid in the whole space , with initial data belonging to . We prove that the system admits a unique local strong solution in , where is independent of the Rossby and Mach numbers. Moreover, using Strichartz-type estimates, we prove the longtime existence of the solution, \emph{i.e.} its lifespan is of the order of , without any smallness assumption on the initial data (the initial data can even go to infinity in some sense), provided that the rotation is fast enough
On the influence of gravity on density-dependent incompressible periodic fluids
Get PDFThe present work is devoted to the analysis of density-dependent, incompressible fluids in a 3D torus, when the Froude number goes to zero. We consider the very general case where the initial data do not have a zero horizontal average, where we only have smoothing effect on the velocity but not on the density and where we can have resonant phenomena on the domain. We explicitly determine the limit system when and prove its global wellposedness. Finally, we prove that for large initial data, the density-dependent, incompressible fluid system is globally wellposed, provided that is small enough
A Global well-posedness result for the Rosensweig system of ferrofluids
Get PDFIn this Paper we study a Bloch-Torrey regularization of the Rosensweig system for ferrofluids. The scope of this paper is twofold. First of all, we investigate the existence and uniqueness of Leray-Hopf solutions of this model in the whole space .
In the second part of this paper we investigate both the long-time behavior of weak solutions and the propagation of Sobolev regularities in dimension tw
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