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math.AP2023★ 1 cited
Density-dependent incompressible Navier--Stokes equations in critical tent spaces
Raphaël Danchin, Ioann Vasilyev
In this article, we prove the existence of global solutions to the inhomogeneous incompressible Navier--Stokes equations, whenever the initial velocity belongs to a certain subspac…
math.AP2021
On the use of tent spaces for solving PDEs: A proof of the Koch-Tataru theorem
Pascal Auscher, Ioann Vasilyev
In these notes we will present (a part of) the parabolic tent spaces theory and then apply it in solving some PDE's originated from the fluid mechanics. In more details, to our mos…
math.AP2020
Variation on a theme by Kiselev and Nazarov: H{ö}lder estimates for non-local transport-diffusion, along a non-divergence-free BMO field
Ioann Vasilyev, François Vigneron
We prove uniform Hölder regularity estimates for a transport-diffusion equation with a fractional diffusion operator,and a general advection field in BMO, as long as the order of t…