Ladder Theorem for a Leray alpha model of turbulence

TL;DR

This paper investigates the regularity and energy inequalities of solutions to the Modified Leray alpha model of turbulence, demonstrating that smooth initial data lead to infinitely differentiable solutions satisfying ladder inequalities.

Contribution

It establishes the infinite differentiability of solutions for smooth initial data and introduces the ladder inequalities in the context of the Leray alpha turbulence model.

Findings

Solutions are infinitely differentiable with smooth initial data.

Solutions satisfy a sequence of energy inequalities called ladder inequalities.

The model provides insights into turbulence regularity properties.

Abstract

In this paper, we study the Modified Leray alpha model with periodic boundary conditions. We show that when the initial data are infinitely differentiable then the unique solution are infinitely differentiable in space and time. Furthermore, this regular solution verifies a sequence of energy inequalities that is called "ladder inequalities".