A Note on Large Time Behavior of Velocity in the Baratropic Compressible Navier-Stokes Equations

2012/06/20 by Fei Jiang, Jiang, Fei
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.1206.4502

openalex publication_date 2012/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, for periodic initial data with initial density allowed to vanish, Huang and Li [1] establish the global existence of strong and weak solutions for the two-dimensional compressible NavierStokes equations with no restrictions on the size of initial data provided the bulk viscosity coefficient is λ= ρ^βwith β> 4/3. Moreover, the large-time behavior of the strong and weak solutions are also obtained, in which the velocity gradient strongly converges to zero in L² norm. In this note, we further point out that the velocity strongly converges to an equilibrium velocity in H¹ norm, in which the equilibrium velocity is uniquely determined by the initial data. Our result can also be regarded a correction for the result of large-time behavior of velocity in [2].

Citations

• Global well-posedness of 2D compressible Navier-Stokes equations with large data and vacuum

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