3 papers
math.AP2024
On the fractional approach to quadratic nonlinear parabolic systems
Oscar Jarrin, Geremy Loachamin
We introduce a general coupled system of parabolic equations with quadratic nonlinear terms and diffusion terms defined by fractional powers of the Laplacian operator. We develop a…
math.AP2023
From non-local to local Navier-Stokes equations
Oscar Jarrin, Geremy Loachamin
Inspired by some experimental (numerical) works on fractional diffusion PDEs, we develop a rigorous framework to prove that solutions to the fractional Navier-Stokes equations, whi…
math.AP2022
From anomalous to classical diffusion in a non-linear heat equation
Oscar Jarrin, Geremy Loachamin
In this paper, we consider the heat equation with the natural polynomial non-linear term; and with two different cases in the diffusion term. The first case (anomalous diffusion) c…