5 papers · 1 filter
Sharp nonuniqueness for the forced 2D Navier-Stokes and dissipative SQG equations
Francisco Mengual, Marcos Solera
We prove a sharp nonuniqueness result for the forced generalized SQG equation. First, this yields nonunique - energy solutions below the Miura-Ju class. In particular, t…
Unstable vortices, sharp non-uniqueness with forcing, and global smooth solutions for the SQG equation
Ángel Castro, Daniel Faraco, Francisco Mengual +1
We prove non-uniqueness of weak solutions to the forced -SQG equation with Sobolev regularity in the supercritical regime , covering the 2D Euler e…
Localized mixing zone for Muskat bubbles and turned interfaces
Ángel Castro, Daniel Faraco, Francisco Mengual
We construct mixing solutions to the incompressible porous media equation starting from Muskat type data in the partially unstable regime. In particular, we consider bubble and tur…
Dissipative Euler flows for vortex sheet initial data without distinguished sign
Francisco Mengual, László Székelyhidi
We construct infinitely many admissible weak solutions to the 2D incompressible Euler equations for vortex sheet initial data. Our initial datum has vorticity concentrated on a sim…
Degraded mixing solutions for the Muskat problem
Ángel Castro, Daniel Faraco, Francisco Mengual
We prove the existence of infinitely many mixing solutions for the Muskat problem in the fully unstable regime displaying a linearly degraded macroscopic behaviour inside the mixin…