Takahito Kashiwabara

activity

20102026

most citedGlobal Strong Well-posedness of the Three Dimensional Primitive equations in

L^{p}

-spaces

90 citations · 251 across the 30 of their papers we have counts for

collaborators

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18 papers · 1 filter

math.AP2026

Local-in-time strong solvability of Navier--Stokes type variational inequalities by Rothe's method

Takahito Kashiwabara

We consider parabolic variational inequalities in a Hilbert space $V$ , which have a non-monotone nonlinearity of Navier--Stokes type represented by a bilinear operator $B: V \times…

math.AP2026

Single exponential $H^{1}$ -upper bounds for the primitive equations

Takahito Kashiwabara

The three dimensional primitive equations with full viscosity are considered in a horizontally periodic box $Ω$ , which are subject to either the homogeneous Neumann or Dirichlet co…

math.AP2025

On periodic traveling wave solutions with or without phase transition to the Navier-Stokes-Korteweg and the Euler-Korteweg equations

Yoshikazu Giga, Takahito Kashiwabara, Haruki Takemura

The Navier-Stokes-Korteweg and the Euler-Korteweg equations are considered in isothermal setting. These are diffuse interface models of two-phase flow. For the Navier-Stokes-Kortew…

math.AP2024

The well-posedness and regularity of the Non-stationary Stokes and Navier-Stokes equations with the friction-type interface condition

Qi Wang, Takahito Kashiwabara, Guanyu Zhou

The friction-type interface condition (FIC) is introduced to describe the phenomenon of the slip and leak of fluid flow on the interface happens only when the difference of stress…

math.AP2024

$H^{2}$ -regularity for stationary and non-stationary Bingham problems with perfect slip boundary condition

Takeshi Fukao, Takahito Kashiwabara

$H^{2}$ -spatial regularity of stationary and non-stationary problems for Bingham fluids formulated with the pseudo-stress tensor is discussed. The problem is mathematically described…

math.AP2023

The three limits of the hydrostatic approximation

Ken Furukawa, Yoshikazu Giga, Matthias Hieber +3

The primitive equations are derived from the $3 D$ -Navier-Stokes equations by the hydrostatic approximation. Formally, assuming an $ε$ -thin domain and anisotropic viscosit…

math.AP2022

Unique solvability of a crack problem with Signorini-type and Tresca friction conditions in a linearized elastodynamic body

Hiromichi Itou, Takahito Kashiwabara

We consider dynamic motion of a linearized elastic body with a crack subject to a modified contact law, which we call the Signorini contact condition of dynamic type, and to the Tr…

math.AP2021

Justification of the Hydrostatic Approximation of the Primitive Equations in Anisotropic Space $L^\infty_H L^q_{x_3}(\Torus^3)$

Ken Furukawa, Takahito Kashiwabara

The primitive equations are fundamental models in geophysical fluid dynamics and derived from the scaled Navier-Stokes equations. In the primitive equations, the evolution equation…

math.AP2020

The Hydrostatic Approximation for the Primitive Equations by the Scaled Navier-Stokes Equations under the No-Slip Boundary Condition

Ken Furukawa, Yoshikazu Giga, Takahito Kashiwabara

In this paper we justify the hydrostatic approximation of the primitive equations in the maximal $L^{p}$ - $L^{q}$ -setting in the three-dimensional layer domain $Ω= \Torus^2 \times (-1,…

math.AP2018★ 27 cited

Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier-Stokes equations

Ken Furukawa, Yoshikazu Giga, Matthias Hieber +3

Consider the anisotropic Navier-Stokes equations as well as the primitive equations. It is shown that the horizontal velocity of the solution to the anisotropic Navier-Stokes equat…

math.AP2018★ 21 cited

The Hydrostatic Stokes Semigroup and Well-Posedness of the Primitive Equations on Spaces of Bounded Functions

Yoshikazu Giga, Mathis Gries, Matthias Hieber +2

Consider the $3$ -d primitive equations in a layer domain $Ω = G \times (- h, 0)$ , $G = (0, 1)^{2}$ , subject to mixed Dirichlet and Neumann boundary conditions at $z = - h$ and $z = 0$ , respectiv…

math.AP2017★ 33 cited

Analyticity of solutions to the primitive equations

Yoshikazu Giga, Mathis Gries, Matthias Hieber +2

This article presents the maximal regularity approach to the primitive equations. It is proved that the $3 D$ primitive equations on cylindrical domains admit a unique, global stron…

math.AP2017★ 12 cited

The Primitive Equations in the scaling invariant space $L^{\infty} (L^{1})$

Yoshikazu Giga, Mathis Gries, Matthias Hieber +2

Consider the primitive equations on $R^{2} \times (z_{0}, z_{1})$ with initial data $a$ of the form $a = a_{1} + a_{2}$ , where $a_{1} \in B U C_{σ} (R^{2}; L^{1} (z_{0}, z_{1}))$ and $a_2 \in L^\infty_σ(\R^2;L^1(…

math.AP2016★ 42 cited

Global Strong $L^{p}$ Well-Posedness of the 3D Primitive Equations with Heat and Salinity Diffusion

Matthias Hieber, Amru Hussein, Takahito Kashiwabara

Consider the full primitive equations, i.e. the three dimensional primitive equations coupled to the equation for temperature and salinity, and subject to outer forces. It is shown…

math.AP2016

Strong Well-Posedness for a Class of Dynamic Outflow Boundary Conditions for Incompressible Newtonian Flows

Dieter Bothe, Takahito Kashiwabara, Matthias Köhne

Based on energy considerations, we derive a class of dynamic outflow boundary conditions for the incompressible Navier-Stokes equations, containing the well-known convective bounda…

math.AP2015★ 4 cited

Strong Time-Periodic Solutions to the 3D Primitive Equations subject to Arbitrary Large Forces

Giovanni P. Galdi, Matthias Hieber, Takahito Kashiwabara

We show that the three-dimensional primitive equations admit a strong time-periodic solution of period $T > 0$ , provided the forcing term $f \in L^{2} (0, T; L^{2} (Ω))$ is a time-p…

math.AP2015★ 90 cited

Global Strong Well-posedness of the Three Dimensional Primitive equations in $L^{p}$ -spaces

Matthias Hieber, Takahito Kashiwabara

In this article, an $L^{p}$ -approach to the primitive equations is developed. In particular, it is shown that the three dimensional primitive equations admit a unique, global strong…

math.AP2012★ 3 cited

On a strong solution of the non-stationary Navier-Stokes equations under slip or leak boundary conditions of friction type

Takahito Kashiwabara

Strong solutions of the non-stationary Navier-Stokes equations under non-linearized slip or leak boundary conditions are investigated. We show that the problems are formulated by a…

Local-in-time strong solvability of Navier--Stokes type variational inequalities by Rothe's method

Single exponential H1-upper bounds for the primitive equations

On periodic traveling wave solutions with or without phase transition to the Navier-Stokes-Korteweg and the Euler-Korteweg equations

The well-posedness and regularity of the Non-stationary Stokes and Navier-Stokes equations with the friction-type interface condition

H2-regularity for stationary and non-stationary Bingham problems with perfect slip boundary condition

The three limits of the hydrostatic approximation

Unique solvability of a crack problem with Signorini-type and Tresca friction conditions in a linearized elastodynamic body

Justification of the Hydrostatic Approximation of the Primitive Equations in Anisotropic Space $L^\infty_H L^q_{x_3}(\Torus^3)$

The Hydrostatic Approximation for the Primitive Equations by the Scaled Navier-Stokes Equations under the No-Slip Boundary Condition

Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier-Stokes equations

The Hydrostatic Stokes Semigroup and Well-Posedness of the Primitive Equations on Spaces of Bounded Functions

Analyticity of solutions to the primitive equations

The Primitive Equations in the scaling invariant space L∞(L1)

Global Strong Lp Well-Posedness of the 3D Primitive Equations with Heat and Salinity Diffusion

Strong Well-Posedness for a Class of Dynamic Outflow Boundary Conditions for Incompressible Newtonian Flows

Strong Time-Periodic Solutions to the 3D Primitive Equations subject to Arbitrary Large Forces

Global Strong Well-posedness of the Three Dimensional Primitive equations in Lp-spaces

On a strong solution of the non-stationary Navier-Stokes equations under slip or leak boundary conditions of friction type

Single exponential $H^{1}$ -upper bounds for the primitive equations

$H^{2}$ -regularity for stationary and non-stationary Bingham problems with perfect slip boundary condition

The Primitive Equations in the scaling invariant space $L^{\infty} (L^{1})$

Global Strong $L^{p}$ Well-Posedness of the 3D Primitive Equations with Heat and Salinity Diffusion

Global Strong Well-posedness of the Three Dimensional Primitive equations in $L^{p}$ -spaces