32 citations · 142 across the 27 of their papers we have counts for
4 papers · 2 filters
Navier-Stokes equations in a curved thin domain, Part I: uniform estimates for the Stokes operator
Tatsu-Hiko Miura
In the series of this paper and the forthcoming papers [41,42] we study the Navier-Stokes equations in a three-dimensional curved thin domain around a given closed surface under Na…
Navier-Stokes equations in a curved thin domain, Part II: global existence of a strong solution
Tatsu-Hiko Miura
We consider the Navier-Stokes equations in a three-dimensional curved thin domain around a given closed surface under Navier's slip boundary conditions. When the thickness of the t…
Sharp boundary -regularity of optimal transport maps
Tatsuya Miura, Felix Otto
In this paper we develop a boundary -regularity theory for optimal transport maps between bounded open sets with -boundary. Our main result asserts sharp $C^{…
Navier-Stokes equations in a curved thin domain, Part III: thin-film limit
Tatsu-Hiko Miura
We consider the Navier-Stokes equations with Navier's slip boundary conditions in a three-dimensional curved thin domain around a given closed surface. Under suitable assumptions w…