27 citations · 44 across the 17 of their papers we have counts for
17 papers
Almost optimal well-posedness for Chern--Simons gauged sigma model under the Lorenz gauge
Huali Zhang, Jie Zhou
In this paper, we study the low-regularity Cauchy problem for the Chern--Simons gauged sigma model in () under the Lorenz gauge. For , we esta…
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…
Low regularity solutions for the Cauchy problem of the ideal incompressible Magnetohydrodynamics equations
Huali Zhang
In Lagrangian coordinates, the local well-posedness of low regularity solutions is established for an ideal incompressible magnetohydrodynamic (MHD) system subject to a homogeneous…
Strichartz estimates and low regularity solutions of 3D relativistic Euler equations
Huali Zhang
We study the low regularity well-posedness for Cauchy problem of 3D relativistic Euler equations. Firstly, we introduce a new decomposition for relativistic velocity and derive new…
Local well-posedness for incompressible neo-Hookean Elastic equations in almost critical Sobolev spaces
Huali Zhang
Inspired by a pioneer work of Andersson-Kapitanski \cite{AK}, we prove the local well-posedness of the Cauchy problem of incompressible neo-Hookean equations if the initial deforma…
Well-posedness for rough solutions of the 3D compressible Euler equations
Lars Andersson, Huali Zhang
In this paper we prove full local well-posedness for the Cauchy problem for the compressible 3D Euler equation, i.e. local existence, uniqueness, and continuous dependence on initi…
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…
Low regularity solutions of two-dimensional compressible Euler equations with dynamic vorticity
Huali Zhang
By establishing a sharp Strichartz estimate for the velocity and density, we prove the local well-posedness of solutions for the Cauchy problem of two-dimensional compressible Eule…
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…
Global well-posedness of cubic fractional Schrödinger equations in one dimension
Huali Zhang, Shiliang Zhao
In this paper, we consider the Cauchy's problem of global existence and scattering behavior of small, smooth, and localized solutions of cubic fractional Schrödinger equations in o…
Global large, smooth solutions of the 2D surface quasi-geostrophic equations
Huali Zhang, Jinlu Li
In this paper, we prove the global regularity of smooth solutions to 2D surface quasi-geostrophic (SQG) equations with super-critical dissipation for a class of large initial data,…
Blow up of fractional Schrödinger equations on manifolds with nonnegative Ricci curvature
Huali Zhang, Shiliang Zhao
In this paper, the well-posedness of Cauchy's problem of fractional Schrödinger equations with a power type nonlinearity on -dimensional manifolds with nonnegative Ricci curvatu…
Global Large Smooth Solutions for 3-D Hall-magnetohydrodynamics
Huali Zhang
In this paper, the global smooth solution of Cauchy's problem of incompressible, resistive, viscous Hall-magnetohydrodynamics (Hall-MHD) is studied. By exploring the nonlinear stru…
Global smooth solutions of MHD equations with large data
Yurui Lin, Huali Zhang, Yi Zhou
In this paper, we establish the global existence of smooth solutions of the three-dimensional MHD system for a class of large initial data. Both the initial velocity and magnetic f…