THE GLOBAL SOLUTION AND BLOWUP OF A EQUATION MODELED FROM THE WATER WAVE PROBLEM WITH CRITICAL GROWTH

doi:10.1007/s10473-025-0608-6

Abstract

Abstract: 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.

Key words: critical Sobolev exponent, blow up, regularity, long time asymptotic behaviour

CLC Number:

35B33

Zhong TAN, Yiying WANG. THE GLOBAL SOLUTION AND BLOWUP OF A EQUATION MODELED FROM THE WATER WAVE PROBLEM WITH CRITICAL GROWTH[J].Acta mathematica scientia,Series B, 2025, 45(6): 2510-2535.

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