TY - JOUR
AU - Bae, Hantaek
AU - Lee, Woojae
AU - Shin, Jaeyong
DA - 2022/02
UR - https://scholarworks.unist.ac.kr/handle/201301/54604
AB - 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.
LA - 영어
PB - PERGAMON-ELSEVIER SCIENCE LTD
TI - Gevrey regularity and finite time singularities for the Kakutani-Matsuuchi model
DO - 10.1016/j.nonrwa.2021.103415
ER -