Existence of Martingale Solutions to Stochastic Constrained Heat Equation

TL;DR

This paper proves the existence of Martingale solutions for stochastic constrained heat equations, extending previous work and employing advanced probabilistic techniques.

Contribution

It establishes the existence of solutions for a class of stochastic constrained heat equations using novel probabilistic methods.

Findings

Existence of Martingale solutions is proven.

The proof employs compactness, tightness, and Martingale representation.

Extends previous results to more general stochastic constrained heat equations.

Abstract

This article extends the work on stochastic constrained heat equation in \cite{brzezniak2020global}. We will show the existence of Martingale solutions to the stochastic-constrained heat equations. The proof is based on compactness, tightness of measure, quadratic variations, and Martingale representation theorem.