Blowup criterion for the Cauchy problem of 2D compressible viscous micropolar fluids with vacuum

Abstract

In this study, we establish a regular criterion for the 2D compressible micropolar viscous fluids with vacuum that is independent of the velocity of rotation of the microscopic particles. Specifically, we show that if the density verifies $ \|\rho\|_{L^\infty(0, T; L^\infty)} < \infty $, then the strong solution will exist globally on $ \Bbb R^2\times(0, T) $. Consequently, we generalize the results of Zhong (Discrete Contin. Dyn. Syst. Ser. B, 25 (2020), no. 12, 4603–4615) to the compressible case. In particular, we don't need the additional compatibility condition.

Keywords

• compressible micropolar fluids
• strong solutions
• vacuum
• cauchy problem
• blowup criterion