A direct approach to nonuniqueness and failure of compactness for the SQG equation. (13th May 2021)

• Record Type: Journal Article
• Authors: Isett, Philip; Ma, Andrew
• Is Part Of: Nonlinearity. Volume 34:Number 5(2021)
• Page Start: 3122
• Page End: 3162
• Publication Date: 2021-05-13
• Subjects: weak solutions -- surface quaisgeostrophic equation -- SQG -- h-principle -- nonuniqueness -- Onsager conjecture; 35Q86; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/abe732
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We give an alternative proof of the nonuniqueness of weak solutions to the surface quasigeostrophic equation (SQG) first shown in [3 ]. Our approach proceeds directly at the level of the scalar field. Furthermore, we prove that every smooth scalar field with compact support that conserves the integral can be realized as a weak limit of solutions to SQG.