Related papers: A regularity result for the free boundary compress…
We derive a priori estimates for the compressible free-boundary Euler equations with surface tension in three spatial dimensions in the case of a liquid. These are estimates for local existence in Lagrangian coordinates when the initial…
In this paper we establish the incompressible limit for the compressible free-boundary Euler equations with surface tension in the case of a liquid. Compared to the case without surface tension treated recently, the presence of surface…
In this paper, we prove a new type of energy estimates for the compressible Euler's equation with free boundary, with a boundary part and an interior part. These can be thought of as a generalization of the energies in Christodoulou and…
We consider the three-dimensional incompressible free-boundary Euler equations in a bounded domain and with surface tension. Using Lagrangian coordinates, we establish a priori estimates for solutions with minimal regularity assumptions on…
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 prove a priori estimates for the compressible Euler equations modeling the motion of a liquid with moving physical vacuum boundary in an unbounded initial domain. The liquid is under influence of gravity but without surface tension. Our…
We prove that the 3-D compressible Euler equations with surface tension along the moving free-boundary are well-posed. Specifically, we consider isentropic dynamics and consider an equation of state, modeling a liquid, given by Courant and…
In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation…
We consider the evolution of a quantity advected by a compressible flow and subject to diffusion. When this quantity is scalar it can be, for instance, the temperature of the flow or the concentration of some pollutants. Because of the…
We address a free boundary model for the compressible Euler equations where the free boundary, which is elastic, evolves according to a weakly damped fourth order hyperbolic equation forced by the fluid pressure. This system captures the…
This paper develops the geometry and analysis of the averaged Euler equations for ideal incompressible flow in domains in Euclidean space and on Riemannian manifolds, possibly with boundary. The averaged Euler equations involve a parameter…
In this paper, we investigate the uniform regularity of solutions to the 3-dimensional isentropic compressible Navier-Stokes system with free surfaces and study the corresponding asymptotic limits of such solutions to that of the…
The purpose of this note is to give a complete proof of a $C^{0,\alpha}$ regularity result for the pressure for weak solutions of the two-dimensional "incompressible Euler equations" when the fluid velocity enjoys the same type of…
We derive a priori estimates for the incompressible free-boundary Euler equations with surface tension in three spatial dimensions. Working in Lagrangian coordinates, we provide a priori estimates for the local existence when the initial…
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 consider the three-dimensional incompressible magnetohydrodynamics (MHD) equations in a bounded domain with small volume and free moving surface boundary. We establish a priori estimate for solutions with minimal regularity assumptions…
The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. We establish well-posedness with inflow, outflow of…
Entropy stabilization of the compressible Euler system is achieved by adapting the averages that are applied to the density and internal energy variables. The approach achieves non-linear robustness despite the use of simplified symmetric…
We study a free boundary problem which is motivated by a particular case of the flow of a non-Newtonian fluid, with a pressure depending yield stress given by a Drucker-Prager plasticity criterion. We focus on the steady case and…
For the incompressible Euler equations the pressure formally scales as a quadratic function of velocity. We provide several optimal regularity estimates on the pressure by using regularity of velocity in various Sobolev, Besov and Hardy…