Jou Chun Kuo, Yoshihiro Shibata
Published 2023-11-26Version 1
In this paper, we proved the local well-posedness for the Navier-Stokes equtions describing the motion of isotropic barotoropic compressible viscous fluid flow with non-slip boundary conditions, wehre the fluid domain is the half-space in the $N$-dimensional Euclidean space. The density part of solutions and their time derivative belong to $L_1$ in time with some Besov spaces in space and also the velosity parts and their time derivative belong to $L_1$ in time with some Besov spaces in space. We use Lagrange transformation to eliminate the covection term and we use an analytic semgroup approach. Our Stokes semigroup is not only a continuous analytic semigroup but also has an $L_1$ in times maximal regularity with some Besov spaces in space.
Comments: $L_1$ maximal regularity theory in the study of the compressible Navier-Stokes equations was first obtained by Danchin and Tolksdolf. Their argument is an extension of Da Prato and Grisvard theory and they assumed that the fluid domain is bounded. We use some real interpolation arguments and we do not need any boundedness assumption of domains. arXiv admin note: substantial text overlap with arXiv:2311.12331
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