On decay estimates of the 3D nematic liquid crystal flows in critical Besov spaces

Liu, Qiao; Zhao, Jihong

doi:10.1002/mma.3846

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2016

2025

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“…For more research on quenching phenomena for parabolic system with Neumann boundary conditions, we refer readers to [3,5,15,17,19], and some advances in quenching phenomena those days, we refer readers to [1,2,[8][9][10][11] and references therein. In addition, for some research on decay, see [6,12,13] and corresponding references therein.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Quenching for a parabolic system with general singular terms

Pei¹,

Li²

2016

J. Nonlinear Sci. Appl.

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In this paper, we study a parabolic system with general singular terms and positive Dirichlet boundary conditions. Some sufficient conditions for finite-time quenching and global existence of the solutions are obtained, and the blow-up of time-derivatives at the quenching point is verified. Furthermore, under some appropriate hypotheses, we prove that the quenching point is only origin and quenching of the system is non-simultaneous. Moreover, the estimate of quenching rate of the corresponding solution is established in this article.

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