arXiv subjects

Kazuhiro Horihata

Publications and source records attributed to Kazuhiro Horihata.

5 recordsLinked to original sources

arXiv2022

A convergence rate of the discrepancy for Allen-Cahn type equation

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 abbreviated to MAC. After that we introduce its benefit: An improved estimate on the discrepant energy that means the equipartition of the first energy. This equation is obtained by rendering the parameter in Allen-Cahn equation time-dependent and adding a term like Z-transform. Furthermore, we mention the existence of a Brakke's motion through our MAC.

math.AP↗

arXiv2022

A partial boundary regularity and a regularity criterion for Harmonic Heat flow

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 monotonical inequality and a reverse Poincaré inequality. This paper establishes these two energy inequalities near the boundary and then by making the best of them, we discuss a partial boundary regularity. In addition to it, we demonstrate a whole domain's regularity under "the one-sided condition." This has been proposed by S.Hildebrandt and K.-O.Widman.

math.AP↗

arXiv2015

A boundary partial regularity and a regularity criterion for New Harmonic Heat flows

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 flow into spheres. Thanks to this scheme, we establish a few energy inequalities of our flow: (i) monotonical inequalities and (ii) a reverse Poincare inequality at any boundary point. These inequalities (i) and (ii) derive the smaller estimates on the set on noncontinuouspoints for pur flow contrast to the former results. We refer to them by Y. Chen and Y. Chen, J. Li, F. H. Lin. Next we introduce two sufficient condition for the whole domain's regularity for it; The one is a boundary energy smallness and the another is an one-sided condition proposed by S. Hildebrandt and K. O. Widman.

math.AP↗

arXiv2014

On a time-discrete approach to solving Navier-Stokes systems

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 energy inequality, we set some assumption though. This result crucially does not provide any new result, but I believe that by making my scheme is more sophisticated, we can develop the study of Navier-Stokes systems.

math.AP↗

arXiv2014

On a new harmonic heat flow with the reverse Hölder inequalities

This paper first proposes a new approximate scheme to construct a harmonic heat flow $u$ between a parabolic cylinder to a sphere. Y.Chen and M.Struwe have proved an existence and discussed a partial regularity of harmonic heat flows by using Ginzburg-Landau heat flow and passing to the limit of a parameter appeared in the equation. To construct a new harmonic heat flow, we propose a Ginzburg-Landau type heat flow with a time-dependent parameter. and we next establish the existence of a harmonic heat flow into spheres with (i) a global energy inequality, (ii) a monotonicity for the scaled energy, (ii) a reverse Poincare inequality. These inequalities (i), (ii) and (iii) improves the Hausdorff dimensional estimates on it's singular set contrast to the former results. I believe that inequalities (i), (ii) and (iii) allow us to analyze how it behaves around its singularities.

math.AP↗