On the pathwise uniqueness of stochastic 2D Euler equations with Kraichnan noise and L^p-data

2024/06/11 by Jiao, Shuaijie, Luo, Dejun
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2406.07167

Abstract

In the recent work [arXiv:2308.03216], Coghi and Maurelli proved pathwise uniqueness of solutions to the vorticity form of stochastic 2D Euler equation, with Kraichnan transport noise and initial data in L¹∩ L^p for p>3/2. The aim of this note is to remove the constraint on p, showing that pathwise uniqueness holds for all L¹∩ L^p initial data with arbitrary p>1.

Related

• Existence and uniqueness by Kraichnan noise for 2D Euler equations with unbounded vorticity
• Weak well-posedness by transport noise for a class of 2D fluid dynamics equations
• Well-posedness for a stochastic 2D Euler equation with transport noise
• Stochastic incompressible Euler equations in a two-dimensional domain
• Existence for stochastic 2D Euler equations with positive H^-1 vorticity