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

Chenchen Lu; Lin Chen; Shaoyong Lai; Chenchen Lu; Lin Chen; Shaoyong Lai

doi:10.3934/math.2024059

AIMS Mathematics

2024, Volume 9, Issue 1: 1199-1210. doi: 10.3934/math.2024059

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

1.
School of Mathematics and Statistics, Yili Normal University, Yining 835000, China
2.
School of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China

Received: 21 October 2023 Revised: 24 November 2023 Accepted: 04 December 2023 Published: 07 December 2023
MSC : 35Q35, 35Q51

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.
- shallow water wave equation,
- local well-posedness,
- blow-up criterion,
- Besov space
Citation: Chenchen Lu, Lin Chen, Shaoyong Lai. Local well-posedness and blow-up criterion to a nonlinear shallow water wave equation[J]. AIMS Mathematics, 2024, 9(1): 1199-1210. doi: 10.3934/math.2024059

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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.

References

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