2019/09/29 by Jincheng Gao, Gao, Jincheng, Zeyu Lyu +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1909.13269
openalex publication_date 2019/09/29 · openalex created_date 2019/10/03 · openalex updated_date 2026/07/28
In this paper, we address the lower bound and space-time decay rates for the compressible Navier-Stokes and Hall-MHD equations under H3-framework in ℝ3. First of all, the lower bound of decay rate for the density, velocity and magnetic field converging to the equilibrium status in L2 is (1+t)-(3)/(4); the lower bound of decay rate for the first order spatial derivative of density and velocity converging to zero in L2 is (1+t)-(5)/(4), and the k(∈ [1, 3])-th order spatial derivative of magnetic field converging to zero in L2 is (1+t)-(3+2k)/(4). Secondly, the lower bound of decay rate for time derivatives of density and velocity converging to zero in L2 is (1+t)-(5)/(4); however, the lower bound of decay rate for time derivatives of magnetic field converging to zero in L2 is (1+t)-(7)/(4). Finally, we address the decay rate of solution in weighted Sobolev space H3γ. More precisely, the upper bound of decay rate of the k(∈ [0, 2])-th order spatial derivatives of density and velocity converging to the k(∈ [0, 2])-th order derivatives of constant equilibrium in weighted space L2γ is t-(3)/(4)+γ-(k)/(2); however, the upper bounds of decay rate of the k(∈ [0, 3])-th order spatial derivatives of magnetic field converging to zero in weighted space L2γ is t-(3)/(4)+(γ)/(2)-(k)/(2).