Dynamics of Partial Differential Equations

Volume 18 (2021)

Number 1

Strong solutions to the Cauchy problem of two-dimensional nonhomogeneous micropolar fluid equations with nonnegative density

Pages: 49 – 69

DOI: https://dx.doi.org/10.4310/DPDE.2021.v18.n1.a4


Xin Zhong (School of Mathematics and Statistics, Southwest University, Chongqing, China)


We consider the Cauchy problem of nonhomogeneous micropolar fluid equations with zero density at infinity on the whole space $\mathbb{R}^2$. By weighted energy method, we show the local existence and uniqueness of strong solutions provided that the initial density decays not too slowly at infinity.


nonhomogeneous micropolar fluid equations, strong solutions, Cauchy problem, nonnegative density

2010 Mathematics Subject Classification

Primary 35Q35. Secondary 76D03.

Received 3 February 2020

Published 19 February 2021