The Cauchy problem for the barotropic compressible Navier--Stokes equations on the whole two-dimensional space with vacuum as far field density is considered. When the shear viscosity is a positive constant and the bulk one is a power function of density with the power bigger than four-thirds, the global existence and uniqueness of strong and classical solutions is established. It should be remarked that there are no restrictions on the size of the data.
Publication:
SIAM Journal on Mathematical Analysis Vol. 54, No. 3(2022), pp. 3192--3214
Author:
Xiangdi Huang
Academy of Mathematics & Systems Science and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, P. R. China.
Email: xdhuang@amss.ac.cn
Jing Li
Department of Mathematics, and Institute of Mathematics and Interdisciplinary Sciences, Nanchang University, Nanchang 330031, P. R. China; Institute of Applied Mathematics, AMSS, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, P. R. China; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China.
Email: ajingli@gmail.com