5 papers
A convergence rate of the discrepancy for Allen-Cahn type equation
Kazuhiro Horihata
This paper presents a new partial differential equation to build Brakke's motion, which is a weak notion of mean curvature flow. We call the equation a modified Allen-Cahn equation…
A partial boundary regularity and a regularity criterion for Harmonic Heat flow
Kazuhiro Horihata
In my previous paper I have contrived a Ginzburg-Landau heat flow with a time-dependent parameter and by using it, I constructed a harmonic heat flow into spheres with a monotonica…
A boundary partial regularity and a regularity criterion for New Harmonic Heat flows
Kazuhiro Horihata
In my previaou paper of K. Horihata, we have proposed a Ginzburg-Landau system with a time-dependent parameter and then passing to the limit we have constructed a harmonic heat flo…
On a time-discrete approach to solving Navier-Stokes systems
Kazuhiro Horihata
We present a new scheme for solving Navier-Stokes systems. This is inspired by material differentiation and combined with discrete Morse semi-flow. The solution has the first energ…
On a new harmonic heat flow with the reverse Hölder inequalities
Kazuhiro Horihata
This paper first proposes a new approximate scheme to construct a harmonic heat flow between a parabolic cylinder to a sphere. Y.Chen and M.Struwe have proved an existence and…