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arXiv · 2410.16468

On regularity of solutions to the Navier--Stokes equation with initial data in $\mathrm{BMO}^{-1}$

Hedong Hou
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Abstract

We prove that any mild solution in the Koch--Tataru space to the incompressible Navier--Stokes equation with initial data in $\mathrm{BMO}^{-1}$ is weak*-continuous in time, valued in $\mathrm{BMO}^{-1}$. We also show that the global mild solution vanishes in $\mathrm{BMO}^{-1}$ at infinity in time.

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Hedong Hou. 2024-10-21. On regularity of solutions to the Navier--Stokes equation with initial data in $\mathrm{BMO}^{-1}$. https://doi.org/10.1137/24m1719487

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