On the Structure of General Weak Solutions of 3D Decaying Turbulence

TL;DR

This paper investigates the properties of weak solutions to 3D decaying turbulence, demonstrating that solutions with decreasing kinetic energy adhere to the strong energy inequality and analyzing their temporal behavior.

Contribution

It establishes that weak solutions with decreasing kinetic energy satisfy the strong energy inequality and provides a comprehensive analysis of their time evolution without extra regularity assumptions.

Findings

Weak solutions with decreasing kinetic energy satisfy the strong energy inequality.

The paper analyzes the temporal behavior of all weak solutions without additional regularity.

Provides insights into the structure of weak solutions in 3D decaying turbulence.

Abstract

It is shown that a weak solution with monotone-decreasing kinetic energy satisfies the strong energy inequality. Using this criterion, we analyze the behavior with respect to time for all weak solutions without any further assumption on regularity.