On uniqueness for a rough transport-diffusion equation

TL;DR

This paper proves the uniqueness of solutions for a transport-diffusion equation with rough coefficients within a low-regularity function space, advancing understanding of such equations under minimal regularity assumptions.

Contribution

It establishes the uniqueness of solutions for a rough transport-diffusion equation in low-regularity settings, which was previously unresolved.

Findings

Solutions are unique in a low-regularity class.

The result applies to equations with rough coefficients.

Advances the theory of transport-diffusion equations under minimal regularity.

Abstract

In this Note, we study a transport-diffusion equation with rough coefficients and we prove that solutions are unique in a low-regularity class.