18 citations · 52 across the 16 of their papers we have counts for
16 papers
Blow-up of the critical norm for a supercritical semilinear heat equation
Hideyuki Miura, Jin Takahashi
We consider the scaling critical Lebesgue norm of blow-up solutions to the semilinear heat equation in an arbitrary smooth domain of . In the rang…
Local regularity conditions on initial data for local energy solutions of the Navier-Stokes equations
Kyungkeun Kang, Hideyuki Miura, Tai-Peng Tsai
We study the regular sets of local energy solutions to the Navier-Stokes equations in terms of conditions on the initial data. It is shown that if a weighted norm of the init…
An -regularity criterion and estimates of the regular set for Navier-Stokes flows in terms of initial data
Kyungkeun Kang, Hideyuki Miura, Tai-Peng Tsai
We prove an -regularity criterion for the 3D Navier-Stokes equations in terms of initial data. It shows that if a scaled local norm of initial data is sufficiently small a…
Short time regularity of Navier-Stokes flows with locally initial data and applications
Kyungkeun Kang, Hideyuki Miura, Tai-Peng Tsai
We prove short time regularity of suitable weak solutions of 3D incompressible Navier-Stokes equations near a point where the initial data is locally in . The result is applie…
On stability of blow-up solutions of the Burgers vortex type for the Navier-Stokes equations with a linear strain
Yasunori Maekawa, Hideyuki Miura, Christophe Prange
We study the three-dimensional Navier-Stokes equations in the presence of the axisymmetric linear strain, where the strain rate depends on time in a specific manner. It is known th…
Local energy weak solutions for the Navier-Stokes equations in the half-space
Yasunori Maekawa, Hideyuki Miura, Christophe Prange
The purpose of this paper is to prove the existence of global in time local energy weak solutions to the Navier-Stokes equations in the half-space . Such solutions a…
Estimates for the Navier-Stokes equations in the half-space for non localized data
Yasunori Maekawa, Hideyuki Miura, Christophe Prange
This paper is devoted to the study of the Stokes and Navier-Stokes equations, in a half-space, for initial data in a class of locally uniform Lebesgue integrable functions, namely…
Green tensor of the Stokes system and asymptotics of stationary Navier-Stokes flows in the half space
Kyungkeun Kang, Hideyuki Miura, Tai-Peng Tsai
We derive refined estimates of the Green tensor of the stationary Stokes system in the half space. We then investigate the spatial asymptotics of stationary solutions of the incomp…
The growth of the vorticity gradient for the two-dimensional Euler flows on domains with corners
Tsubasa Itoh, Hideyuki Miura, Tsuyoshi Yoneda
We consider the two-dimensional Euler equations in non-smooth domains with corners. It is shown that if the angle of the corner is strictly less than , the Lipschitz estim…
On uniqueness for the Harmonic Map Heat Flow in supercritical dimensions
Pierre Germain, Tej-Eddine Ghoul, Hideyuki Miura
We examine the question of uniqueness for the equivariant reduction of the harmonic map heat flow in the energy supercritical dimension. It is shown that, generically, singular dat…
Remark on single exponential bound of the vorticity gradient for the two-dimensional Euler flow around a corner
Tsubasa Itoh, Hideyuki Miura, Tsuyoshi Yoneda
In this paper, the two dimensional Euler flow under a simple symmetry condition with hyperbolic structure in a unit square …
Remark on the Helmholtz decomposition in domains with noncompact boundary
Yasunori Maekawa, Hideyuki Miura
Let be a domain with noncompact boundary. It is known that the Helmholtz decomposition is not always valid in except for the energy space . In this paper we c…
On Poisson operators and Dirichlet-Neumann maps in H^s for divergence form elliptic operators with Lipschitz coefficients
Yasunori Maekawa, Hideyuki Miura
We consider second order uniformly elliptic operators of divergence form in whose coefficients are independent of one variable. Under the Lipschitz condition on the coef…
On domain of Poisson operators and factorization for divergence form elliptic operators
Yasunori Maekawa, Hideyuki Miura
We consider second order uniformly elliptic operators of divergence form in whose coefficients are independent of one variable. For such a class of operators we establis…
Asymptotics of small exterior Navier-Stokes flows with non-decaying boundary data
Kyungkuen Kang, Hideyuki Miura, Tai-Peng Tsai
We prove the unique existence of solutions of the 3D incompressible Navier-Stokes equations in an exterior domain with small non-decaying boundary data, for or $t \in (0,…
Point singularities of 3D stationary Navier-Stokes flows
Hideyuki Miura, Tai-Peng Tsai
This article characterizes the singularities of very weak solutions of 3D stationary Navier-Stokes equations in a punctured ball which are sufficiently small in weak .