Year: 2026
Type: article
Abstract: We study the incompressible Euler equation and prove that the set of weak solutions is path-connected. More precisely, we construct paths of Hölder regularity $$C^{1/2}$$ C 1 / 2 , valued in $$C^0_{t, loc} L^2_x$$ C t , l o c 0 L x 2 endowed with the strong topology. The main result relies on a convex integration construction adapted from the seminal work of De Lellis and Székelyhidi (Ann of Math (2) 170:1417-1436, 2009), extending it to a more broader geometric framework, replacing balls with arbitrary convex compact sets.
Source: Journal of Evolution Equations
Author: Philippe Anjolras
Institution: Université Paris-Saclay
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W7124744972