32 citations · 142 across the 27 of their papers we have counts for
28 papers
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…
General rigidity principles for stable and minimal elastic curves
Tatsuya Miura, Kensuke Yoshizawa
For a wide class of curvature energy functionals defined for planar curves under the fixed-length constraint, we obtain optimal necessary conditions for global and local minimizers…
Pinned planar p-elasticae
Tatsuya Miura, Kensuke Yoshizawa
Building on our previous work, we classify all planar -elasticae under the pinned boundary condition, and then obtain uniqueness and geometric properties of global minimizers. A…
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…
Li-Yau type inequality for curves in any codimension
Tatsuya Miura
For immersed curves in Euclidean space of any codimension we establish a Li--Yau type inequality that gives a lower bound of the (normalized) bending energy in terms of multiplicit…
A diameter bound for compact surfaces and the Plateau-Douglas problem
Tatsuya Miura
In this paper we give a geometric argument for bounding the diameter of a connected compact surface (with boundary) of arbitrary codimension in Euclidean space in terms of Topping'…
Polar tangential angles and free elasticae
Tatsuya Miura
In this note we investigate the behavior of the polar tangential angle of a general plane curve, and in particular prove its monotonicity for certain curves of monotone curvature.…
Geometric inequalities involving mean curvature for closed surfaces
Tatsuya Miura
In this paper we prove some geometric inequalities for closed surfaces in Euclidean three-space. Motivated by Gage's inequality for convex curves, we first verify that for convex s…
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…
On the isoperimetric inequality and surface diffusion flow for multiply winding curves
Tatsuya Miura, Shinya Okabe
In this paper we establish a general form of the isoperimetric inequality for immersed closed curves (possibly non-convex) in the plane under rotational symmetry. As an application…
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…
Hamilton--Jacobi equations on an evolving surface
Klaus Deckelnick, Charles M. Elliott, Tatsu-Hiko Miura +1
We consider the well-posedness and numerical approximation of a Hamilton--Jacobi equation on an evolving hypersurface in . Definitions of viscosity sub- and supersolut…
Elastic curves and phase transitions
Tatsuya Miura
This paper is devoted to classical variational problems for planar elastic curves of clamped endpoints, so-called Euler's elastica problem. We investigate a straightening limit tha…
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-…