5 papers
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…
Remark on the scattering theory of the nonlinear Schrödinger equation on the cylinders
Xing Cheng, Jiqiang Zheng
In this article, we consider the nonlinear Schrödinger equation on the cylinder . In the long range case, we show there is no linear scattering state…
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…