Related papers: Physical Vacuum Problems for the Full Compressible…
This article is concerned with the local well-posedness problem for the compressible Euler equations in gas dynamics. For this system we consider the free boundary problem which corresponds to a physical vacuum. Despite the clear physical…
In this paper we provide a complete local well-posedness theory for the free boundary relativistic Euler equations with a physical vacuum boundary on a Minkowski background. Specifically, we establish the following results: (i) local…
An important problem in gas and fluid dynamics is to understand the behavior of vacuum states, namely the behavior of the system in the presence of vacuum. In particular, physical vacuum, in which the boundary moves with a nontrivial finite…
An important problem in the theory of compressible gas flows is to understand the singular behavior of vacuum states. The main difficulty lies in the fact that the system becomes degenerate at the vacuum boundary, where the characteristics…
We provide a complete local well-posedness theory in $H^s$ based Sobolev spaces for the free boundary incompressible Euler equations with zero surface tension on a connected fluid domain. Our well-posedness theory includes: (i) Local…
We consider the local well-posedness of the one-dimensional nonisentropic Euler equations with moving physical vacuum boundary condition. The physical vacuum singularity requires the sound speed to be scaled as the square root of the…
This paper is concerned with the three dimensional compressible Euler--Poisson equations with moving physical vacuum boundary condition. This fluid system is usually used to describe the motion of a self-gravitating inviscid gaseous star.…
The present paper aims to establish the local well-posedness of Euler's fluid equations on geometric rough paths. In particular, we consider the Euler equations for the incompressible flow of an ideal fluid whose Lagrangian transport…
In this paper, we present a novel Eulerian-Lagrangian formulation for the compressible isentropic Euler equations with vaccum. Using the developed Lagrangian flow map formulation, we show a short-time solution for a general pressure law. A…
This paper is concerned with the 1-D compressible Euler-Poisson equations with moving physical vacuum boundary condition. It is usually used to describe the motion of a self-gravitating inviscid gaseous star. The local well-posedness of…
We show that the incompressible Euler equations on $\mathbb{R}^2$ are not locally well-posed in the sense of Hadamard in the Besov space $B^1_{\infty,1}$. Our approach relies on the technique of Lagrangian deformations of Bourgain and Li.…
This paper concerns the well-posedness theory of the motion of physical vacuum for the compressible Euler equations with or without self-gravitation. First, a general uniqueness theorem of classical solutions is proved for the three…
We consider the Cauchy problem to the barotropic compressible Navier-Stokes equations. We obtain optimal local well-posedness in the sense of Hadamard in the critical Besov space $\mathbb{X}_p=\dot{B}_{p,1}^{\frac{d}{p}}\times…
We consider the 3D compressible isentropic Euler equations describing the motion of a liquid in an unbounded initial domain with a moving boundary and a fixed flat bottom at finite depth. The liquid is under the influence of gravity and…
We prove a local in time existence and uniqueness theorem of classical solutions of the coupled Einstein--Euler system, and therefore establish the well posedness of this system. We use the condition that the energy density might vanish or…
We prove well-posedness for the 3-D compressible Euler equations with moving physical vacuum boundary, with an equation of state given by the so-called gamma gas-law for gamma > 1. The physical vacuum singularity requires the sound speed c…
We provide a new method for treating free boundary problems in perfect fluids, and prove local-in-time well-posedness in Sobolev spaces for the free-surface incompressible 3D Euler equations with or without surface tension for arbitrary…
We establish the local well-posedness for the free boundary problem for the compressible Euler equations describing the motion of liquid under the influence of Newtonian self-gravity. We do this by solving a tangentially-smoothed version of…
We present a local existence result for the three dimensional incompressible Euler equations. The solution is constructed using a formulation of the equations as an active vector system in Eulerian coordinates. The formulation employs the…
We study the free boundary problem for the equations of compressible Euler equations with a vacuum boundary condition. Our main goal is to recover in Eulerian coordinates the earlier well-posedness result obtained by Lindblad [Lindblad H.,…