摘要
We consider the global well-posedness of strong solutions to the Cauchy problem of compressible barotropic Navier-Stokes equations in R^(2). By exploiting the global-in-time estimate to the two-dimensional(2D for short) classical incompressible Navier-Stokes equations and using techniques developed in(SIAM J Math Anal, 2020, 52(2): 1806–1843), we derive the global existence of solutions provided that the initial data satisfies some smallness condition. In particular, the initial velocity with some arbitrary Besov norm of potential part Pu_0 and large high oscillation are allowed in our results. Moreover, we also construct an example with the initial data involving such a smallness condition, but with a norm that is arbitrarily large.
作者
翟小平
钟新
Xiaoping ZHAI;Xin ZHONG(School of Mathematics and Statistics,Guangdong University of Technology,Guangzhou,510520,China;School of Mathematics and Statistics,Southwest University,Chongqing,400715,China)
基金
Zhai was partially supported by the Guangdong Provincial Natural Science Foundation (2022A1515011977)
the Science and Technology Program of Shenzhen(20200806104726001)
Zhong was partially supported by the NNSF of China (11901474, 12071359)
the Exceptional Young Talents Project of Chongqing Talent (cstc2021ycjh-bgzxm0153)。
