4 papers
Low regularity ill-posedness and shock formation for 3D ideal compressible MHD
Xinliang An, Haoyang Chen, Silu Yin
The study of magnetohydrodynamics (MHD) significantly boosts the understanding and development of solar physics, planetary dynamics and controlled nuclear fusion. Dynamical propert…
The Cauchy problems for the 2D compressible Euler equations and ideal MHD system are ill-posed in
Xinliang An, Haoyang Chen, Silu Yin
In a fractional Sobolev space with , we prove the low-regularity ill-posedness for the 2D compressible Euler equations and the 2D ideal compressib…
Shock Formation for Compressible Euler Equations on
Xinliang An, Haoyang Chen, Fulin Qi +1
In this paper, we prove the finite-time shock formation for the compressible Euler equations on the two-dimensional sphere . In contrast to the flat Euclidean case $\…
Low-Regularity Local Well-Posedness for the Elastic Wave System
Xinliang An, Haoyang Chen, Sifan Yu
We study the elastic wave system in three spatial dimensions. For admissible harmonic elastic materials, we prove a desired low-regularity local well-posedness result for the corre…