Global well-posedness and large-time behavior for anisotropic inhomogeneous Navier-Stokes equations with mixed partial dissipation
Year: 2025
Type: article
Abstract: In this paper, we consider the Cauchy problem for the two-dimensional anisotropic inhomogeneous Navier-Stokes equations with mixed partial dissipation, where the density at infinity is in the state $ \widetilde{\rho} > 0 $. We obtain the global well-posedness of strong solutions and the large-time behavior of the velocity field under the condition that $ \Vert \sqrt{\rho_0} \mathbf{u}_0 \Vert_{L^2} $ is sufficiently small. It is worth noting that our results include the case of vacuum.
Source: Electronic Research Archive
DOI: 10.3934/era.2025194
Author: Ying Wang
Institution: Guangxi University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,000
OpenAlex ID: W4412581247