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

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.

arXiv comment17 pages. An easier proof of Proposition 3.3 (Proposition 3.2 in version 1) is presented. A remark on sharpness of the results is provided. Comments are welcome

References in corpus (2)

• Numerical investigations of non-uniqueness for the Navier-Stokes initial value problem in borderline spaces
• On well-posedness for parabolic Cauchy problems of Lions type with rough initial data

Cited by in corpus (1)

• Non-Uniqueness of Smooth Solutions of the Navier-Stokes Equations from Critical Data