Related papers: Global existence for partially dissipative hyperbo…
We prove global existence of strong solutions for the Vlasov-Poisson system in a convex bounded domain in the plasma physics case assuming homogeneous Dirichlet boundary conditions for the electric potential and the specular reflection…
We consider a two-dimensional MHD model describing the evolution of viscous, compressible and electrically conducting fluids under the action of vertical magnetic field without resistivity. Existence of global weak solutions is established…
A new framework to obtain time-decay estimates for partially dissipative hyperbolic systems set on the real line is developed. Under the classical Shizuta-Kawashima (SK) stability condition, equivalent to the Kalman rank condition in…
We apply a Lyapunov function to obtain conditions for the existence and uniqueness of small classical time-periodic solutions to first order quasilinear 1D hyperbolic systems with (nonlinear) nonlocal boundary conditions in a strip. The…
This paper solves the global well-posedness and stability problem on a special $2\frac12$-D compressible viscous non-resistive MHD system near a steady-state solution. The steady-state here consists of a positive constant density and a…
In the paper, we consider a multi-dimensional bipolar hydrodynamic model from semiconductor devices and plasmas. This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equations. We show…
In this paper, we study the problem of global existence of weak solutions for the quasi-stationary compressible Stokes equations with an anisotropic viscous tensor. The key element of our proof is the control of a particular defect measure…
We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…
We prove the global existence of weak solutions to the isentropic compressible Navier-Stokes equations with ripped density in the half-plane under a slip boundary condition provided the bulk viscosity coefficient is properly large.…
The global well-posedness and stability of solutions to the three-dimensional compressible Euler equations with damping is a longstanding open problem. This problem was addressed in \cite{WY, STW} in the isentropic regime (i.e. $\gamma>1$)…
We study global existence and decay estimates for quasilinear wave equations with dissipative terms in the Sobolev space $H^L \times H^{L-1}$, where $L \geq [d/2]+3$. The linear dissipative terms depend on space variable coefficient, and…
We study existence and regularity properties of solutions to the singular $p$-Laplacean parabolic system in a bounded domain $\Omega$. The main purpose is to prove global $L^r(\varepsilon,T;L^q(\Omega))$, $\varepsilon\geq0$, integrability…
This paper studies the global existence and uniqueness of strong solutions and its large-time behavior for the compressible isothermal Euler equations with a nonlocal dissipation. The system is rigorously derived from the kinetic…
We prove existence of $L^2$-weak solutions of a quasilinear wave equation with boundary conditions. This describes the isothermal evolution of a one dimensional non-linear elastic material, attached to a fixed point on one side and subject…
To circumvent the ill-posedness issues present in various models of continuum fluid mechanics, we present a dynamical systems approach aiming at selection of physically relevant solutions. Even under the presence of infinitely many…
This paper is devoted to confront two different approaches to the problem of dynam-ical perfect plasticity. Interpreting this model as a constrained boundary value Friedrichs' system enables one to derive admissible hyperbolic boundary…
We demonstrate the global existence of weak solutions to a class of semilinear strongly damped wave equations possessing nonlinear hyperbolic dynamic boundary conditions. Our work assumes $(-\Delta_W)^\theta \partial_tu$ with…
The work is devoted to the relaxation limit in larger Besov spaces for compressible Euler equations, which contains previous results in Sobolev spaces and Besov spaces with critical regularity. Such an extension depends on a revision of…
In this paper, we establish the global existence of Lagrangian solutions to the ionic Vlasov--Poisson system under mild integrability assumptions on the initial data. Our approach involves proving the well-posedness of the…
This article is devoted to the study of the critical dissipative surface quasi-geostrophic $(SQG)$ equation in $\mathbb{R}^2$. For any initial data $\theta_{0}$ belonging to the space $\Lambda^{s} ( H^{s}_{uloc}(\mathbb{R}^2)) \cap…