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Bae, Hantaek
School of Natural Science
Research Interests
  • Fluid dynamics, polymeric fluid, kinetic theory

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Gevrey regularity and finite time singularities for the Kakutani-Matsuuchi model

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Title
Gevrey regularity and finite time singularities for the Kakutani-Matsuuchi model
Author
Bae, HantaekLee, WoojaeShin, Jaeyong
Issue Date
2022-02
Publisher
PERGAMON-ELSEVIER SCIENCE LTD
Citation
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v.63, pp.103415
Abstract
In this paper, we deal with the Kakutani-Matsuuchi model which describes the surface elevation eta of the water-waves under the effect of viscosity. We first derive the decay rate of weak solutions. This can be used to obtain the decay rate of parallel to eta(t)parallel to (<(H)over dot>1) when initial data is sufficiently small in <(H)over dot>(1). We next show the existence, uniqueness, Gevrey regularity and decay rates of eta with sufficiently small initial data in B-2,1(1). To do so, we derive a commutator estimate involving Gevrey operator. We then apply our method to the supercritical quasi-geostrophic equations. We finally show the formation of singularities of smooth solutions in finite time for a certain class of initial data . (C) 2021 Elsevier Ltd. All rights reserved.
URI
https://scholarworks.unist.ac.kr/handle/201301/54604
URL
https://www.sciencedirect.com/science/article/pii/S1468121821001279?via%3Dihub
DOI
10.1016/j.nonrwa.2021.103415
ISSN
1468-1218
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