Yuxi Zheng

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math.AP2005

On Asymptotic Variational Wave Equations

Alberto Bressan, Ping Zhang, Yuxi Zheng

We investigate the equation $(u_{t} + (f (u))_{x})_{x} = f^{''} (u) (u_{x})^{2} /2$ where $f (u)$ is a given smooth function. Typically $f (u) = u^{2} /2$ or $u^{3} /3$ . This equation models unidirectional…

math.AP1998

Axisymmetric Solutions of the Euler Equations for Sub-Square Polytropic Gases

Yuxi Zheng, Tong Zhang

We establish rigorously the existence of a three-parameter family of self-similar,globally bounded, and continuous weak solutions in two space dimensions to the compressible Euler…