Communications in Mathematical Sciences

Volume 19 (2021)

Number 4

Long time existence of the Boussinesq equation with large initial data in $\mathbb{R}^n$

Pages: 1137 – 1147

DOI: https://dx.doi.org/10.4310/CMS.2021.v19.n4.a12

Authors

Guowei Liu (School of Mathematical Sciences, Chongqing Normal University, Chongqing, China)

Wenlong Sun (School of Information and Mathematics, Yangtze University, Jingzhou, China)

Abstract

In this paper, we study the long-time existence of smooth solutions to the Cauchy problem for the Boussinesq equation with large initial data in $\mathbb{R}^n$. Due to the strong dispersive effect in the Boussinesq equation, the method of combining the blowup criterion and Strichartz estimate are used to show that the lifespan of the solutions can be taken arbitrarily large provided that the dispersive coefficient is large enough.

Keywords

Boussinesq equation, dispersion, blowup criterion, Strichartz estimate

2010 Mathematics Subject Classification

35B40, 35Q35, 76D99

Full Text (PDF format)

The first author is supported by the National Nature Science Foundation of China (Grant No. 12001073), the Natural Science Foundation of Chongqing (Grant No. cstc2020jcyjmsxmX0709), the Natural Science Foundation of Chongqing (Grant Nos. cstc2020jcyjjqX0022 and cstc2018jcyjAX0010) and the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN201900543).

The second author is supported by the 2020 Higher Career Development Program (Grant No. 7010702801), the Innovation training program for college Students (Grant No. 2019367) and the National Nature Science Foundation of China (Grant No. 61673006).

Received 28 October 2019

Accepted 21 December 2020

Published 18 June 2021