A uniqueness lemma with applications to regularization and incompressible fluid mechanics

• 作者: Guillaume Lévy
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2021,（4）
• 所属期刊栏目: Articles
• 页码范围: 711-724
• 页数: 14页
• 语种: 英文

摘要

In this paper,we extend our previous result from Lévy (2016).We prove that transport equations with rough coefficients do possess a uniqueness property,even in the presence of viscosity.Our method relies strongly on duality and bears a strong resemblance to the well-known DiPerna-Lions theory first developed by DiPerna and Lions (1989).This uniqueness result allows us to reprove the celebrated theorem of Serrin (1962) in a novel way.As a byproduct of the techniques,we derive an L1 bound for the vorticity in terms of a critical Lebesgue norm of the velocity field.We also show that the zero solution is unique for the 2D Euler equations on the torus under a mild integrability assumption.