Axisymmetric weak solutions to stationary compressible Navier-Stokes equations with critical indices
Analysis of PDEs
2024-10-24 v3
Abstract
This paper studies the isothermal stationary compressible Navier-Stokes equations on global space and cylinder domains. There are two critical exponents in such settings: The heat ratio 1 is an end point of the classical theory on weak solutions; the axisymmetric solutions in the global domain involve the critical index of Sobolev's inequality. Some new observations based on the cancellation structure of the equations are collected to get over these obstacles due to critical exponents.
Keywords
Cite
@article{arxiv.2311.13791,
title = {Axisymmetric weak solutions to stationary compressible Navier-Stokes equations with critical indices},
author = {Xinyu Fan and Song Jiang},
journal= {arXiv preprint arXiv:2311.13791},
year = {2024}
}