L₁ approach to the compressible viscous fluid flows in the half-space

2023/11/21 by Jou chun Kuo, Yoshihiro Shibata, Kuo, Jou chun +1
Earth and Planetary Sciences · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2311.12331

openalex publication_date 2023/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the local well-posedness for the Navier-Stokes equations describing the motion of isotropic barotoropic compressible viscous fluid flow with non-slip boundary conditions, where the fluid domain is the N dimensional half-sapce. We solve the equations in the L₁ in time and Besov spaces B^s_q,1 in space maximal regularity framework. Here, we assume that -1+N/q ≤ s < 1/q and N-1 < q < 2N. We use Lagrange transformation to eliminate the convection term and we use an analytic semigroup approach. We only assume the strictly positiveness of initial mass density.

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