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math.AP2025
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…
math.AP2025
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…
math.AP2025
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…