Related papers: BV solutions constructed by epsilon-neighborhood m…
This paper is concerned with an approximation scheme for rate-independent systems governed by a non-smooth dissipation and a possibly non-convex energy functional. The scheme is based on the local minimization scheme introduced in [EM06],…
This article is the third one in a series of papers by the authors on vanishing-viscosity solutions to rate-independent damage systems. While in the first two papers [KRZ13, KRZ15] the assumptions on the spatial domain $\Omega$ were kept as…
We establish local-in-time existence and uniqueness results for nonlocal conservation laws with a nonlinear mobility, in several space dimensions, under weak assumptions on the kernel, which is assumed to be bounded and of finite total…
Let a 1-d system of hyperbolic conservation laws, with two unknowns, be endowed with a convex entropy. We consider the family of small $BV$ functions which are global solutions of this equation. For any small $BV$ initial data, such global…
We are concerned with multidimensional stochastic balance laws. We identify a class of nonlinear balance laws for which uniform spatial $BV$ bounds for vanishing viscosity approximations can be achieved. Moreover, we establish temporal…
We investigate the global existence of weak solutions to a free boundary problem governing the evolution of finitely extensible bead-spring chains in dilute polymers. The free boundary in the present context is defined with regard to a…
Several mechanical systems are modeled by the static momentum balance for the displacement $u$ coupled with a rate-independent flow rule for some internal variable $z$. We consider a class of abstract systems of ODEs which have the same…
In this paper we consider the Navier-Stokes equations supplemented with either the Dirichlet or vorticity-based Navier boundary conditions. We prove that weak solutions obtained as limits of solutions to the Navier-Stokes-Voigt model…
We describe recent results obtained by G. Barles, P. Cardaliaguet, R. Monneau and the author recently. They are concerned with nonlocal Eikonal equations arising in the study of the dynamics of dislocation lines in crystals. These equations…
This paper is dedicated to the construction of global weak solutions to the quantum Navier-Stokes equation, for any initial value with bounded energy and entropy. The construction is uniform with respect to the Planck constant. This allows…
We show that under some appropriate assumptions, every weak solution (e.g. energetic solution) to a given rate-independent system is of class SBV, or has finite jumps, or is even piecewise $C^1$. Our assumption is essentially imposed on the…
This paper is devoted to the study of the nonlinear stability of the rarefaction waves of the Vlasov-Poisson-Boltzmann system with slab symmetry in the case where the electron background density satisfies an analogue of the Boltzmann…
Solutions to hyperbolic conservation laws can be approximated in many different ways: by vanishing viscosity, relaxations, discrete or semi-discrete numerical schemes, approximation with a nonlocal flux, etc$\ldots$ For some of these…
We give a new concise proof of a certain one-scale epsilon regularity criterion using weak-strong uniqueness for solutions of the Navier-Stokes equations with non-zero boundary conditions. It is inspired by an analogous approach for the…
In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…
The global existence of martingale solutions to the compressible Navier-Stokes equations driven by stochastic external forces, with density-dependent viscosity and vacuum, is established in this paper. This work can be regarded as a…
We study the vanishing viscosity method for the eikonal equation $|Du|=V$ in $B(0,1)$ with homogeneous Dirichlet boundary value condition. By assuming $V$ is radially symmetric and restricting attention to radially symmetric solutions, we…
The paper aims on the construction of weak solutions to equations of a model of compressible viscous fluids, being a simplification of the classical compressible Navier-Stokes system. We present a novel scheme for approximating systems that…
In this paper we prove the existence of global weak dissipative martingale solutions for a one-dimensional compressible fluid model with capillarity and density dependent viscosity, driven by random initial data and a stochastic forcing…
We study the two-dimensional incompressible Navier-Stokes equations in a channel $\Omega=(0,L)\times(0,H)$ with small viscosity $\varepsilon\ll1$, an $\varepsilon$-Navier slip condition on the horizontal walls, and a viscous inflow…