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math.AP2024
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…
math.AP2024
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…
math.AP2024
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…