Persistence properties and wave-breaking criteria for a generalized two-component rotational b-family system

Meiling Yang; Yongsheng Li; Zhijun Qiao

doi:10.3934/dcds.2020122

Article Contents

2020, Volume 40, Issue 4: 2475-2493. Doi: 10.3934/dcds.2020122

This issue Previous Article Equicontinuity, transitivity and sensitivity: The Auslander-Yorke dichotomy revisited Next Article Supercritical elliptic problems on the round sphere and nodal solutions to the Yamabe problem in projective spaces

Persistence properties and wave-breaking criteria for a generalized two-component rotational b-family system

1.
School of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, China
2.
School of Mathematical and Statistical Science, University of Texas Rio Grande Valley, Edinburg, TX 78539, USA

^*Corresponding author: Zhijun Qiao
^*Corresponding author: Zhijun Qiao

Received: July 1, 2019

Revised: November 1, 2019

Published online: April 1, 2020

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Abstract

In this paper, we investigate a generalized two-component rotational b-family system arising in the rotating fluid with the effect of the Coriolis force. First, we study the persistence properties of the system in weighted $ L^p $-spaces, for a large class of moderate weights. Secondly, in order to overcome the difficulty arising from higher order nonlinearity and no conservation law, we take the advantage of the specially intrinsic structure of the system and make use of commutator estimate, and then derive two blow-up results for the strong solutions to the system.

Keywords:

Generalized two-component rotational b-family system,
Cauchy problem,
persistence properties,
blow-up,
weighted spaces.

Mathematics Subject Classification: Primary: 35B35, 35B44, 35D35.

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