Spatial-decay of solutions to the quasi-geostrophic equation with the critical and supercritical dissipation
Spatial-decay of solutions to the quasi-geostrophic equation with the critical and supercritical dissipation
复制标题
具有临界和超临界耗散的准地转方程解的空间衰变
DOI：
10.1088/1361-6544/ab0e5a
复制
发表时间：
2019
期刊：
影响因子：
1.7
通讯作者：
Sugiyama Yuusuke
中科院分区：
文献类型：
--
作者：
Yamamoto Masakazu;Sugiyama Yuusuke
研究了地球物理流体动力学二维耗散准地转方程的初值问题。该方程的耗散由分数拉普拉斯算子给出。众所周知，半拉普拉斯算子是准地转方程的临界耗散。在适当条件下解的全局存在性也是众所周知的，并且随着空间变量趋于无穷大，分数耗散方程的解以多项式阶数衰减。本文给出了临界和超临界情况下准地转方程解的远场渐近性。这些估计是从解及其渐近轮廓之间差异的能量方法得出的。
The initial value problem for the two-dimensional dissipative quasi-geostrophic equation derived from geophysical fluid dynamics is studied. The dissipation of this equation is given by the fractional Laplacian. It is known that the half Laplacian is a critical dissipation for the quasi-geostrophic equation. The global existence of solutions upon the suitable condition is also well known, and that solutions of a fractional dissipative equation decay with a polynomial order as the spatial variable tends to infinity. In this paper, far field asymptotics of solutions to the quasi-geostrophic equation are given in the critical and the supercritical cases. Those estimates are derived from the energy methods for the difference between the solution and its asymptotic profile.