Related papers: Dynamical relativistic liquid bodies
We introduce a new wave formulation for the relativistic Euler equations with vacuum boundary conditions that consists of a system of non-linear wave equations in divergence form with a combination of acoustic and Dirichlet boundary…
We demonstrate that a sufficiently smooth solution of the relativistic Euler equations that represents a dynamical compact liquid body, when expressed in Lagrangian coordinates, determines a solution to a system of non-linear wave equations…
We prove the local existence of solutions to the Einstein-Elastic equations that represent self-gravitating, relativistic elastic bodies with compact support.
We prove a local existence theorem for the free boundary problem for a relativistic fluid in a fixed spacetime. Our proof involves an a priori estimate which only requires control of derivatives tangential to the boundary, which holds also…
We prove the existence of a wide class of solutions to the isentropic relativistic Euler equations in 2 spacetime dimensions with an equation of state of the form $p=K\rho^2$ that have a fluid vacuum boundary. Near the fluid vacuum…
We study the relativistic Euler equations on the Minkowski spacetime background. We make assumptions on the equation of state and the initial data that are relativistic analogs of the well-known physical vacuum boundary condition, which has…
We introduce a damping term for the special relativistic Euler equations in $3$-D and show that the equations reduce to the non-relativistic damped Euler equations in the Newtonian limit. We then write the equations as a symmetric…
We consider the Euler equations governing relativistic compressible fluids evolving in the Minkowski spacetime with several spatial variables. We propose a new symmetrization which makes sense for solutions containing vacuum states and, for…
We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent…
The Euler equations governing a relativistic perfect fluid are put into symmetric hyperbolic form with dependent variables the fluid's specific entropy plus a generalized velocity vector equal to the fluid's unit relativistic velocity…
We consider elastic bodies in rigid rotation, both nonrelativistically and in special relativity. Assuming a body to be in its natural state in the absence of rotation, we prove the existence of solutions to the elastic field equations for…
We explore the relationship between mechanical systems describing the motion of a particle with the mechanical systems describing a continuous medium. More specifically, we will study how the so-called intermediate integrals or fields of…
Exploring the general analytical solutions to the Euler equations for ideal fluids holds significant theoretical and practical importance. The steady flows in two-dimensional spaces are considered whether there is an analytical solution in…
I review recent and not so recent progress on formulating and numerically implementing a consistent set of relativistic equations which describe the space-time evolution of viscous relativistic fluids without violating causality.
In this note we consider the motion of a solid body in a two dimensional incompressible perfect fluid. We prove the global existence of solutions in the case where the initial vorticity belongs to $L^p$ with $p>1$ and is compactly…
Some classical and recent results on the Euler equations governing perfect (incompressible and inviscid) fluid motion are collected and reviewed, with some small novelties scattered throughout. The perspective and emphasis will be given…
This paper presents an alternative {\it relativistic nonlinear} approach to the vacuum case of classical electrodynamics. Our view is based on the understanding that the corresponding differential equations should be dynamical in nature.…
We study the rest-frame instant form of a new formulation of relativistic perfect fluids in terms of new generalized Eulerian configuration coordinates. After the separation of the relativistic center of mass from the relative variables on…
We study the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion. More specifically, we prove the existence of local solutions to the relativistic Boltzmann equation that are nearby the local…
We investigate the initial-value problem for the relativistic Euler equations governing isothermal perfect fluid flows, and generalize an approach introduced by LeFloch and Shelukhin in the non-relativistic setting. We establish the…