Optimal decay rate for the 2-D compressible Oldroyd-B and Hall-MHD model

Abstract

In this paper, we are concerned with long time behavior of the strong solutions to the 2-D compressible Oldroyd-B and Hall-MHD model. By virtue of the improved Fourier splitting method and the time weighted energy estimate, we obtain the $L^2$ decay rate $(1+t{)}^{-\frac{1}{4}}$. According to the Littlewood-Paley theory, we prove that the solutions belong to the critical Besov space with negative index. Finally, we show optimal decay rate in $H^2$-framework without the smallness restriction of low frequencies.

arXiv comment23 pages. arXiv admin note: text overlap with arXiv:2107.10418

References in corpus (4)

• Global Existence and Large-Time Behavior of Solutions to the Three-Dimensional Equations of Compressible Magnetohydrodynamic Flows
• Global solutions to the three-dimensional full compressible magnetohydrodynamic flows
• Global Solutions for Incompressible Viscoelastic Fluids
• Optimal decay for the compressible MHD equations in the critical regularity framework