相关论文: Incompressible limit for the 2D isentropic Euler s…
In this paper, we explore the low Mach number singular limit of the local-in-time strong solutions to the compressible primitive equations with gravity for general adiabatic coefficient. First we construct the uniform estimate for the…
We establish the global existence of weak solutions of the isentropic compressible magnetohydrodynamic equations with ripped density in the whole plane provided the bulk viscosity coefficient is properly large. Moreover, we show that such…
We consider a singular limit problem for the complete compressible Euler system in the low Mach and strong stratification regime. We identify the limit problem - the anelastic Euler system - in the case of well prepared initial data. The…
This paper is concerned with the incompressible limit of the compressible magnetohydrodynamic equations with vanishing viscosity coefficients and general initial data in the whole space $\mathbb{R}^d$ $ (d=2$ or 3). It is rigorously showed…
This paper concerns the low Mach number limit of weak solutions to the compressible Navier-Stokes equations for isentropic fluids in a bounded domain with a Navier-slip boundary condition. In \cite{DGLM99}, it has been proved that if the…
In this paper we deal with the Cauchy problem for the incompressible Euler equations in the three-dimensional periodic setting. We prove non-uniqueness for an $L^2$-dense set of H\"older continuous initial data in the class of H\"older…
The Euler system in fluid dynamics is a model of a compressible inviscid fluid incorporating the three basic physical principles: Conservation of mass, momentum, and energy. We show that the Cauchy problem is basically ill-posed for the…
In this article we study the limit when $\alpha \to 0$ of solutions to the $\alpha$-Euler system in the half-plane, with no-slip boundary conditions, to weak solutions of the 2D incompressible Euler equations with non-negative initial…
This paper is concerned with the Riemann problem for the two-dimensional barotropic compressible Euler system with a general strictly increasing pressure law. By means of convex integration, the existence of infinitely many admissible weak…
We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper we show that,…
This paper studies a singular limit problem for a reduced model for compressible non-resistive MHD which was first introduced in \cite{Li-Sun_JDE, Li-Sun} in a two-dimensional setting. This system can also be related to a certain class of…
We consider the compressible Navier-Stokes system describing the motion of a viscous fluid confined to a straight layer $\Omega_{\delta}=(0,\delta)\times\mathbb{R}^2$. We show that the weak solutions in the 3D domain converge strongly to…
In the present paper, we show an improved lower bound for the lifespan of the solutions to the ideal MHD equations in the case of space dimension $d=2$. In particular, for small initial magnetic fields $b_0$ of size (say) $\varepsilon>0$,…
In this short note we partially extend the recent nonuniqueness results on admissible weak solutions to the Riemann problem for the 2D compressible isentropic Euler equations. We prove nonuniqueness of admissible weak solutions that start…
IIn the paper, we consider the inviscid, incompressible and semiclassical limits limits of the barotropic quantum Navier-Stokes equations of compressible flows in a periodic domain. We show that the limit solutions satisfy the…
We investigate the low Mach number limit for the 3-D quantum Navier-Stokes system. For general ill-prepared initial data, we prove strong convergence of finite energy weak solutions to weak solutions of the incompressible Navier-Stokes…
In the present paper, we consider the compressible Navier--Stokes--Korteweg system on the $2$D whole plane and show that a unique global solution exists in the scaling critical Fourier--Besov spaces for arbitrary large initial data provided…
The present paper is devoted to the well-posedness issue for a low-Mach number limit system with heat conduction but no viscosity. We will work in the framework of general Besov spaces $B^s_{p,r}(\R^d)$, $d\geq 2$, which can be embedded…
For the 2D compressible isentropic Euler equations of polytropic gases with an initial perturbation of size $\ve$ of a rest state, it has been known that if the initial data are rotationnally invariant or irrotational, then the lifespan…
We study the low Mach number limit for a viscous compressible two-fluid model with algebraic pressure closure in the three-dimensional torus $\mathbb{T}^3$. The pressure is determined implicitly through the densities of the two phases,…