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The linearized Israel-Stewart equations with a physical vacuum boundary

Runzhang Zhong

Abstract

In this article, we consider the Israel-Stewart equations of relativistic viscous fluid dynamics with bulk viscosity. We investigate the evolution of the equations linearized about solutions that satisfy the physical vacuum boundary condition and establish local well-posedness of the corresponding Cauchy problem.

The linearized Israel-Stewart equations with a physical vacuum boundary

Abstract

In this article, we consider the Israel-Stewart equations of relativistic viscous fluid dynamics with bulk viscosity. We investigate the evolution of the equations linearized about solutions that satisfy the physical vacuum boundary condition and establish local well-posedness of the corresponding Cauchy problem.

Paper Structure

This paper contains 12 sections, 14 theorems, 175 equations.

Table of Contents

  1. Introduction
  2. The Equations of Motion
  3. Physical Vacuum Boundary
  4. Basic energy estimate for the linearized equations
  5. The Linearized Equations
  6. Function Spaces
  7. Basic Energy Estimate
  8. Local wellposedness of linearized equations and its high-order estimate
  9. Bookkeeping Scheme
  10. Weighted Elliptic Operators
  11. Elliptic Estimates
  12. Local Wellposedness of the Linearized Equations

Key Result

Lemma 2.3

Assume that $j_1>j_2 \geq 0$ and $\sigma_1>\sigma_2>-\frac{1}{2}$ with $j_1-j_2=\sigma_1-\sigma_2$. Then we have

Theorems & Definitions (32)

  • Definition 2.1
  • Definition 2.2
  • Lemma 2.3
  • Corollary 2.4
  • Corollary 2.5
  • Lemma 2.8
  • proof
  • Lemma 2.9
  • proof
  • Remark 2.10
  • ...and 22 more