The global strong solution to compressible system with fractional viscous term
Analysis of PDEs
2024-07-03 v2
Abstract
In this paper, we study the Cauchy problem to the 3D fractional compressible isentropic generalized Navier-Stokes equations for viscous compressible fluid with one Levy diffusion process. We obtain the existence and uniqueness of global strong solution for small initial data by providing several commutators via the Littlewood-Paley theory. Moreover, we derive -decay rate for the highest derivative of the strong solution without decay loss by using a cancellation of a low-medium-frequency quantity. Our results improve the results provided in [J. Differential Equations 377(2023): 369-417].
Keywords
Cite
@article{arxiv.2311.11877,
title = {The global strong solution to compressible system with fractional viscous term},
author = {Mengqian Liu and Lei Niu and Zhigang Wu},
journal= {arXiv preprint arXiv:2311.11877},
year = {2024}
}