6 papers
Multi-dimensional centered rarefaction waves of gas dynamics with vacuum states
Jin Jia, Tao Luo
We establish the local-in-time structural stability of two centered rarefaction waves bounding a vacuum region for the two-dimensional isentropic Euler equations with ,…
Hadamard Local Well-Posedness for Compressible Liquids with a Free Surface
Tao Luo, Ruixi Zhang
We prove local well-posedness in the Hadamard sense for the three-dimensional compressible Euler equations governing a liquid with a free surface and no surface tension. Under the…
Low-regularity a priori estimates, blow-up criterion, and self-intersection singularities for free-boundary ideal magnetohydrodynamics with surface tension
Tao Luo, Siqi Yang
We study the three-dimensional incompressible free-boundary ideal magnetohydrodynamic (MHD) equations with surface tension and a closed free surface. Our first result establishes $…
Multi-Dimensional Structural Stability of Mixed Riemann Configurations Containing Centered Rarefaction Waves and Surfaces of Discontinuities of Gas Dynamics
Jin Jia, Tao Luo
For 2D compressible Euler equations of isentropic gas, we prove the structural stability of mixed Riemann configurations containing centered rarefaction waves and surfaces of disco…
Classification of finite-time blow-up mechanisms for the incompressible free-boundary Euler equations with surface tension
Chengchun Hao, Tao Luo, Siqi Yang
We establish a blow-up criterion for strong solutions of the three-dimensional incompressible Euler equations with surface tension in a bounded domain with a closed moving free bou…
Exponential stability of a free boundary problem with spherical symmetry for a gas bubble immersed in a bounded incompressible liquid
Chengchun Hao, Tao Luo, Siqi Yang
This paper is mainly concerned with the free boundary problem for an approximate model (for example, arising from the study of sonoluminescence) of a gas bubble of finite mass encl…