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Research Article | Open Access

Local well-posedness and blow-up criterion to a nonlinear shallow water wave equation

Chenchen Lu1, Lin Chen1, Shaoyong Lai2( )
School of Mathematics and Statistics, Yili Normal University, Yining 835000, China
School of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China
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Abstract

The initial data problem to a nonlinear shallow water wave equation in nonhomogeneous Besov space is discussed. Using the decomposition of Littlewood-Paley and the properties of nonhomogeneous Besov space, we establish the well-posedness of short time solutions for the equation in the Besov space. A blow-up criterion of solutions is also obtained.

Keywords

shallow water wave equationlocal well-posednessblow-up criterionBesov space
CLC number: 35Q35, 35Q51

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AIMS Mathematics
Volume 9 Issue 1,
January 2024
Pages 1199-1210
DOI: 10.3934/math.2024059

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Cite this article:
Lu C, Chen L, Lai S. Local well-posedness and blow-up criterion to a nonlinear shallow water wave equation. AIMS Mathematics, 2024, 9(1): 1199-1210. https://doi.org/10.3934/math.2024059

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Received: 21 October 2023
Revised: 24 November 2023
Accepted: 04 December 2023
Published: 15 January 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)