7 papers · 1 filter
Low Regularity Well-Posedness of Cauchy Problem for Two-Dimensional Relativistic Euler Equation
Huali Zhang
In this article, we initiate the study of the Cauchy problem for the two-dimensional relativistic Euler equations in a low-regularity setting. By introducing good variables--a resc…
Improved Local Well-Posedness in Sobolev Spaces for Two-Dimensional Compressible Euler Equations
Huali Zhang
We establish the local existence and uniqueness of solutions to the two-dimensional compressible Euler equations with initial velocity $\bv_0$, logarithmic density , and speci…
Local well-posedness for Chern-Simons gauged sigma equations under the Lorenz gauge
Jin Guanghui, Huali Zhang
In this paper, we study the Cauchy problem for the Chern-Simons gauged sigma model under the Lorenz gauge condition. We prove the local well-posedness of solutions if the in…
On the rough solutions of 3D compressible Euler equations: an alternative proof
Huali Zhang, Lars Andersson
The well-posedness of Cauchy problem of 3D compressible Euler equations is studied. By using Smith-Tataru's approach \cite{ST}, we prove the local existence, uniqueness and stabili…
On 3D Hall-MHD equations with fractional Laplacians: global well-posedness
Huali Zhang, Kun Zhao
Cauchy problem for 3D incompressible Hall-magnetohydrodynamics (Hall-MHD) system with fractional Laplacians is studied. First, global well-posedness of small-energy solutions with…
A class of global large, smooth solutions for the magnetohydrodynamics with the Hall and ion-slip effects
Huali Zhang
In this paper, the Cauchy's problem for fractional MHD system with the Hall and ion-slip effects is considered. By exploring the structure of semilinear and quasilinear terms, we p…