LOCAL STRONG SOLUTIONS TO THE NONHOMOGENEOUS BENARD SYSTEM WITH NONNEGATIVE DENSITY

被引：8
作者：
Zhong, Xin [1 ]
机构：
[1] Southwest Univ, Sch Math & Stat, Chongqing, Peoples R China
来源：
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2020年 / 50卷 / 04期
关键词：
nonhomogeneous Benard system; strong solutions; Cauchy problem; nonnegative density; GLOBAL WELL-POSEDNESS; NAVIER-STOKES EQUATIONS; EXISTENCE; BOUNDARY;
D O I：
10.1216/rmj.2020.50.1497
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the Cauchy problem of the nonhomogeneous Benard system in the whole two-dimensional (2D) space, where the density is allowed to vanish initially. We prove that there exists a unique local strong solution. To compensate for the lack of integrability of the velocity in the whole space, a careful space weight is imposed on the initial density, which cannot decay too slowly in the far field.
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页码：1497 / 1516
页数：20
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