Global existence and stability of near-affine solutions of compressible elastodynamics

2025/12/18 by Hu, Xianpeng, Tu, Yuanzhi, Wang, Changyou +1
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.16505

Abstract

We prove that for sufficiently small H³-perturbations of an affine solution, the Cauchy problem for the compressible nonlinear elastodynamics in ℝ^d, for d=2,3, admits a unique global strong solution. Moreover, we establish the asymptotic behavior of the solution.

Citations

• Vanishing viscosity limits for the free boundary problem of compressible viscoelastic fluids with surface tension
• Global existence of near-affine solutions to the compressible Euler equations
• Expanding large global solutions of the equations of compressible fluid mechanics
• Global existence for the 2D incompressible isotropic elastodynamics for small initial data
• Global Well-posedness of Incompressible Elastodynamics in Two Dimensions
• Global Well‐Posedness of Incompressible Elastodynamics in Two Dimensions
• Almost Global Existence for 2-D Incompressible Isotropic Elastodynamics
• Almost global existence for 2-D incompressible isotropic elastodynamics
• Global Existence for the Multi-Dimensional Compressible Viscoelastic flows
• On almost global existence for nonrelativistic wave equations in 3D

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• Global strong solutions to the compressible Navier--Stokes--Coriolis system for large data