32 citations · 142 across the 27 of their papers we have counts for
18 papers · 1 filter
Approximation of a solution to the stationary Navier-Stokes equations in a curved thin domain by a solution to thin-film limit equations
Tatsu-Hiko Miura
We consider the stationary Navier-Stokes equations in a three-dimensional curved thin domain around a given closed surface under the slip boundary conditions. Our aim is to show th…
Migrating elastic flows
Tomoya Kemmochi, Tatsuya Miura
Huisken's problem asks whether there is an elastic flow of closed planar curves that is initially contained in the upper half-plane but `migrates' to the lower half-plane at a posi…
Error estimate for classical solutions to the heat equation in a moving thin domain and its limit equation
Tatsu-Hiko Miura
We consider the Neumann type problem of the heat equation in a moving thin domain around a given closed moving hypersurface. The main result of this paper is an error estimate in t…
Nonlinear stability of the two-jet Kolmogorov type flow on the unit sphere under a perturbation with nondissipative part
Tatsu-Hiko Miura
We consider the vorticity form of the Navier-Stokes equations on the two-dimensional unit sphere and study the nonlinear stability of the two-jet Kolmogorov type flow which is a st…
Delta-convex structure of the singular set of distance functions
Tatsuya Miura, Minoru Tanaka
For the distance function from any closed subset of any complete Finsler manifold, we prove that the singular set is equal to a countable union of delta-convex hypersurfaces up to…
Complete classification of planar p-elasticae
Tatsuya Miura, Kensuke Yoshizawa
Euler's elastica is defined by a critical point of the total squared curvature under the fixed length constraint, and its -counterpart is called -elastica. In this paper we…
Rate of the enhanced dissipation for the two-jet Kolmogorov type flow on the unit sphere
Yasunori Maekawa, Tatsu-Hiko Miura
We study the enhanced dissipation for the two-jet Kolmogorov type flow which is a stationary solution to the Navier-Stokes equations on the two-dimensional unit sphere given by the…
Optimal thresholds for preserving embeddedness of elastic flows
Tatsuya Miura, Marius Müller, Fabian Rupp
We consider elastic flows of closed curves in Euclidean space. We obtain optimal energy thresholds below which elastic flows preserve embeddedness of initial curves for all time. T…
Linear stability and enhanced dissipation for the two-jet Kolmogorov type flow on the unit sphere
Tatsu-Hiko Miura
We consider the Navier-Stokes equations on the two-dimensional unit sphere and study the linear stability of the two-jet Kolmogorov type flow which is a stationary solution given b…
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…
Navier--Stokes equations in a curved thin domain
Tatsu-Hiko Miura
We consider the three-dimensional incompressible Navier--Stokes equations in a curved thin domain with Navier's slip boundary conditions. The curved thin domain is defined as a reg…
On singular limit equations for incompressible fluids in moving thin domains
Tatsu-Hiko Miura
We consider the incompressible Euler and Navier-Stokes equations in a three-dimensional moving thin domain. Under the assumption that the moving thin domain degenerates into a two-…
A characterization of cut locus for hypersurfaces
Tatsuya Miura
Let be an open set in with -boundary and be the skeleton of , which consists of points where the distance function to is not differentiab…
Singular perturbation by bending for an adhesive obstacle problem
Tatsuya Miura
A free boundary problem arising from materials science is studied in one-dimensional case. The problem studied here is an obstacle problem for the non-convex energy consisting of a…
An example of a mean-convex mean curvature flow developing infinitely many singular epochs
Tatsuya Miura
In this paper, we give an example of a compact mean-convex hypersurface with a single singular point moved by mean curvature having a sequence of singular epochs (times) converging…