Path-connectedness of incompressible Euler solutions
Abstract
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.
Fields of Study & Subjects
Navier-Stokes equation solutions
Advanced Mathematical Physics Problems
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Journal of Evolution Equations
- Volume
- 26
- Issue
- 1
- Publication date
- 19 January 2026
- Language
- EN