5 papers
Singular limits for general energy-critical complex Ginzburg-Landau equations
Lingbang Gao, Jie Xin, Yunrui Zheng
Motivated by dissipative approximations of the three-dimensional focusing energy-critical nonlinear Schrödinger equation, we study the inviscid and zero-dispersion limits for gener…
Global well-posedness of the energy-critical complex Ginzburg-Landau equation in exterior domains
Xing Cheng, Chang-Yu Guo, Jiqiang Zheng +1
In this article, we consider an energy-critical complex Ginzburg-Landau equation in the exterior of a smooth compact strictly convex obstacle. We prove the global well-posedness of…
Stability of Navier-Stokes equations with a free surface
Xing Cheng, Yunrui Zheng
We consider the viscous incompressible fluids in a three-dimensional horizontally periodic domain bounded below by a fixed smooth boundary and above by a free moving surface. The f…
Threshold solutions of the energy-critical complex Ginzburg-Landau equation
Xing Cheng, Yunrui Zheng
In this article, we consider energy-critical complex Ginzburg-Landau equation in three and four dimensions. We give the dynamics when the energy of the initial data is equal to the…
The limit theory of the energy-critical complex Ginzburg-Landau equation
Xing. Cheng, Chang-yu Guo, Yunrui. Zheng
We study the limit behavior of the solutions to energy-critical complex Ginzburg-Landau equation. We give a rigorous theory of the zero-dispersion limit from energy-critical comple…