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<p>In this paper, 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 energy-critical complex Ginzburg-Landau equation in an exterior domain by the concentration-compactness/rigidity theorem method. As corollaries of our main result, we establish both the existence of global weak solutions to energy-critical defocusing nonlinear Schrödinger equation and the global well-posedness theory for energy-critical semi-linear heat equation in exterior domains.</p>

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Global well-posedness of the energy-critical complex Ginzburg-Landau equation in exterior domains

  • 期刊论文

  • 发表日期：

    2025年10月15日

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  • Xing Cheng,
  • Chang-Yu Guo,
  • Jiqiang Zheng,
  • Yunrui Zheng

摘要

In this paper, 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 energy-critical complex Ginzburg-Landau equation in an exterior domain by the concentration-compactness/rigidity theorem method. As corollaries of our main result, we establish both the existence of global weak solutions to energy-critical defocusing nonlinear Schrödinger equation and the global well-posedness theory for energy-critical semi-linear heat equation in exterior domains.