Temperature patches for the subcritical Boussinesq-Navier-Stokes System with no diffusion
Calvin Khor, Xiaojing Xu
TL;DR
This paper proves that temperature patches in the subcritical Boussinesq-Navier-Stokes system without diffusion maintain their boundary regularity over time, extending previous results to all subcritical viscosities.
Contribution
It generalizes the preservation of boundary regularity for temperature patches to the entire subcritical viscosity range in the no-diffusion Boussinesq-Navier-Stokes system.
Findings
Temperature patch boundaries remain Hölder continuous over time.
The result extends previous work to all subcritical viscosities.
Boundary regularity is preserved without diffusion.
Abstract
In this paper, we prove that temperature patch solutions to the subcritical Boussinesq-Navier-Stokes System with no diffusion preserve the H\"older regularity of their boundary for all time, which generalises the previously known result by F. Gancedo and E. Garc\'ia-Ju\'arez [Annals of PDE, 3(2):14, 2017] to the full range of subcritical viscosity.
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Taxonomy
TopicsNavier-Stokes equation solutions · Stability and Controllability of Differential Equations · Nonlinear Partial Differential Equations