Related papers: The stability of simple plane-symmetric shock form…
We prove the existence of a subsonic axisymmetric weak solution $({\bf u},\rho,p)$ with ${\bf u}=u_x{\bf e}_x+u_r{\bf e}_r+u_\theta{\bf e}_{\theta}$ to steady Euler system in a three-dimensional infinitely long cylinder $\mathcal{N}$ when…
This paper shows that for the three-dimensional compressible isentropic Navier-Stokes equations, the planar viscous shocks are time-asymptotically stable to suitably small initial perturbations with zero masses. In particular, the…
We establish the local uniqueness of steady transonic shock solutions with spherical symmetry for the three-dimensional full Euler equations. These transonic shock-fronts are important for understanding transonic shock phenomena in…
We consider the Cauchy problem with smooth data for compressible Euler equations in many dimensions and concentrate on two cases: solutions with finite mass and energy and solutions corresponding to a compact perturbation of a nontrivial…
We study an outflow problem for the $3$-dimensional isentropic compressible Navier-Stokes equations. The fluid under consideration occupies the exterior domain of the unit ball $\Omega=\{x\in\mathbb{R}^3\,\vert\, |x|\ge 1\}$ and it is…
In this paper, we consider the 3-D compressible isentropic MHD equations with infinity electric conductivity. The existence of unique local classical solutions is firstly established when the initial data is arbitrarily large, contains…
We prove the uniqueness and stability of entropy shocks to the isentropic Euler systems among all vanishing viscosity limits of solutions to associated Navier-Stokes systems. To take into account the vanishing viscosity limit, we show a…
We consider Einstein's equations coupled to the Euler equations in plane symmetry, with compact spatial slices and constant mean curvature time. We show that for a wide variety of equations of state and a large class of initial data,…
We present a simulation for the interactions of shockwaves with light spherical density inhomogeneities. Euler equations for two-phase compressible flows are solved in a 3D uniform resolution finite volume based solver using 5th order WENO…
In a previous work with Tai-Peng Tsai, the author studied the dynamics of axisymmetric, swirl-free Euler equation in four and higher dimensions. One conclusion of this analysis is that the dynamics become dramatically more singular as the…
This paper concerns the dynamic stability of the steady 3-D wave structure of a planar normal shock front intersecting perpendicularly to a planar solid wall for unsteady potential flows. The stability problem can be formulated as a free…
The present contribution proves the asymptotic orbital stability of viscous regularizations of stable Riemann shocks of scalar balance laws, uniformly with respect to the viscosity/diffusion parameter $\epsilon$. The uniformity is…
The global well-posedness and stability of solutions to the three-dimensional compressible Euler equations with damping is a longstanding open problem. This problem was addressed in \cite{WY, STW} in the isentropic regime (i.e. $\gamma>1$)…
In this paper, we prove the finite-time shock formation for the compressible Euler equations on the two-dimensional sphere $\mathbb{S}^2$. In contrast to the flat Euclidean case $\mathbb{R}^2$, the geometry of $\mathbb S^2$ imposes new…
We show that the multi-dimensional compressible Euler system for isothermal flow of an ideal, polytropic gas admits global-in-time, radially symmetric solutions with unbounded amplitudes due to wave focusing. The examples are similarity…
In this paper, we study desingularization of steady solutions of 3D incompressible Euler equation with helical symmetry in a general helical domain. We construct a family of steady Euler flows with helical symmetry, such that the associated…
This paper studies the non-implosion mechanism for the 3D incompressible Euler equations. We prove that vorticity blows up in finite time, whereas the $L^p_T L^\infty_{loc}$ $(p\in[1,\infty))$ norm of the velocity field remains bounded.…
It is shown that smooth solutions with small amplitude to the 1D Euler-Poisson system for electrons persist forever with no shock formation.
We prove the stability of three-dimensional axisymmetric solutions to the steady Euler system with transonic shocks in divergent nozzles under perturbations of the exit pressure and the supersonic solution in the upstream region. We first…
We establish the existence and stability of the transonic shock solution to three-dimensional axisymmetric Euler system with an external force in a cylinder under perturbations of the incoming supersonic flow, the exit pressure, the…