Well-posedness of Generalized Fractional Singular Burgers equation driven by $|D|^{\frac{1}{2}}\xi$

TL;DR

This paper establishes the local well-posedness of the Generalized Fractional Singular Burgers equation driven by a fractional derivative of noise, providing a framework for generalized solutions and connecting them to classical solutions.

Contribution

It introduces a framework for generalized solutions of the GFSB and proves its local well-posedness, extending understanding of fractional stochastic PDEs.

Findings

Proved local well-posedness of GFSB

Established the framework for generalized solutions

Connected GFSB solutions to classical solutions for b3 > 3/2

Abstract

In this paper, we study the generalized solution of Fractional Singular Burgers equation driving by $\vert D\vert^{\frac{1}{2}}\xi$. We establish a framework to describe the equations satisfied by generalized solutions, termed the Generalized Fractional Singular Burgers equation(GFSB), and prove its local well-posedness. Finally, we prove that the solution of GFSB can be the generalized solution of Fractional Singular Burgers equation for $\gamma>\frac{3}{2}$.