An almost sure energy inequality for Markov solutions to the 3D Navier-Stokes equations

TL;DR

This paper establishes the existence of Markov solutions to the 3D Navier-Stokes equations that satisfy an almost sure energy inequality, advancing the understanding of their probabilistic and energetic properties.

Contribution

It introduces weak martingale solutions that fulfill an almost sure energy inequality and form an almost sure Markov process, a novel result in the analysis of 3D Navier-Stokes equations.

Findings

Existence of weak martingale solutions with almost sure energy inequality

Solutions form an almost sure Markov process

Advances understanding of probabilistic properties of Navier-Stokes solutions

Abstract

We prove existence of weak martingale solutions satisfying an almost sure version of the energy inequality and which constitute a (almost sure) Markov process.