收录:
摘要:
In this paper, we consider solutions to the incompressible axisymmetric Euler equations without swirl. The main result is to prove the global existence of weak solutions if the initial vorticity w(0)(theta ) satisfies that w(0)(theta/)r is an element of L-1 boolean AND L-p(R-3) for some p > 1. It is not required that the initial energy is finite, that is, the initial velocity u(0) belongs to L-2(R-3) here. We construct the approximate solutions by regularizing the initial data and show that the concentrations of energy do not occur in this case. The key ingredient in the proof lies in establishing the L-loc(2+alpha)(R-3) estimates of velocity fields for some alpha > 0, which is new to the best of our knowledge.
关键词:
通讯作者信息:
电子邮件地址:
来源 :
JOURNAL OF NONLINEAR SCIENCE
ISSN: 0938-8974
年份: 2021
期: 2
卷: 31
3 . 0 0 0
JCR@2022
ESI学科: MATHEMATICS;
ESI高被引阀值:31
JCR分区:1
归属院系: