Work

Flexibility of two-dimensional Euler flows with integrable vorticity

Year: 2026

Type: article

Abstract: We propose a new convex integration scheme in fluid mechanics, and we provide an application to the two-dimensional Euler equations. We prove the flexibility and nonuniqueness of L∞L2 weak solutions with vorticity in L∞Lp for some p>1, surpassing for the first time the critical scaling of the standard convex integration technique. To achieve this, we introduce several new ideas, including: a new family of building blocks built from the Lamb–Chaplygin dipole; a new method to cancel the error based on time averages and nonperiodic, spatially anisotropic perturbations.

Source: Duke Mathematical Journal

DOI: 10.1215/00127094-2025-0056

Authors: Elia Bruè, Maria Colombo, Anuj Kumar

Institutions: Bocconi University, École Polytechnique Fédérale de Lausanne, University of California, Davis

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4406022784

FWCI: 58.71

Cites: 71

Cited by: 43

Related to: 10