2025/01/23 by Alberto Enciso, Enciso, Alberto, Javier Peñafiel-Tomás +3 · 1 citation
Mathematics · #Mathematical Dynamics and Fractals #Navier-Stokes equation solutions #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2501.13632
Given any smooth solenoidal vector field v0 on \mathbf T3, we show the existence of infinitely many Hölder-continuous steady Euler flows v with the same topology as v0, in certain weak sense. In particular, we show that v possesses a unique flow of the highest Hölder regularity, which is conjugate to the flow of v0 via a volume-preserving Hölder homeomorphism of \mathbf T3. This result extends to the case of Euler equations on toroidal domains, which has applications to the study of plasmas. The proof relies on a novel convex integration scheme incorporating the key idea that the velocity field of the subsolutions must remain diffeomorphic to v0 at each iteration step.