On the classical solutions of the three dimensional Stefan problem

TL;DR

This paper investigates the existence of classical solutions to the three-dimensional Stefan problem, employing Friedrich's mollifier to establish global existence in Hölder spaces.

Contribution

It introduces a method using Friedrich's mollifier to prove the global existence of classical solutions for the three-dimensional Stefan problem.

Findings

Established global existence of classical solutions.

Utilized Friedrich's mollifier in Hölder space framework.

Provided a new approach to the Stefan problem.

Abstract

We study the global existence in time and we obtained the classical one with Friedrich's mollifier like the elliptic operator in Holder space.