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<p>In this article, we study the water wave problem with critical growth. We mainly concern with the blowup and asymptotic estimates of the global solution. First, we prove the blow up and decay estimates of the solution with low-energy initial value. Next, we prove the regularity of the global solution with low-energy initial value. In the last part, we study the concentration phenomenon of the global solution no matter with low energy or not by the method of concentration compactness principle.</p>

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The global solution and blowup of a equation modeled from the water wave problem with critical growth

  • 期刊论文

  • 发表日期：

    2025年10月29日

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  • Zhong Tan,
  • Yiying Wang

摘要

In this article, we study the water wave problem with critical growth. We mainly concern with the blowup and asymptotic estimates of the global solution. First, we prove the blow up and decay estimates of the solution with low-energy initial value. Next, we prove the regularity of the global solution with low-energy initial value. In the last part, we study the concentration phenomenon of the global solution no matter with low energy or not by the method of concentration compactness principle.