27 citations · 27 across the 7 of their papers we have counts for
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Solutions to a One-Dimensional Combustion-Type Free Boundary Problem via Maximal Regularity
Ken Furukawa, Yoshikazu Giga, Naoto Kajiwara
We study a one-dimensional free boundary problem arising in combustion theory, where the motion of the interface is governed by a prescribed Neumann boundary flux and a zero Dirich…
No formulation of a new phase for a free boundary problem in combustion theory
Ken Furukawa, Yoshikazu Giga, Naoto Kajiwara
We consider a free boundary problem for the heat equation with a given non-negative external heat source. On the free boundary, we impose the zero Dirichlet condition and the fixed…
The three limits of the hydrostatic approximation
Ken Furukawa, Yoshikazu Giga, Matthias Hieber +3
The primitive equations are derived from the -Navier-Stokes equations by the hydrostatic approximation. Formally, assuming an -thin domain and anisotropic viscosit…
Data Assimilation to the Primitive Equations with --based Maximal Regularity Approach
Ken Furukawa
In this paper, we show mathematical justification of the data assimilation of nudging type in - maximal regularity settings. We prove that the approximate solution of the…
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…
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 --setting in the three-dimensional layer domain $Ω= \Torus^2 \times (-1,…
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…