Non-uniqueness of forced active scalar equations with even drift operators

PDEs in connection with fluid mechanics (35Q35) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) PDEs in connection with geophysics (35Q86)

Cites Work

Unnamed Item
Dissipative continuous Euler flows
Dissipative Euler flows and Onsager's conjecture
Global well-posedness for an advection-diffusion equation arising in magneto-geostrophic dynamics
Lack of uniqueness for weak solutions of the incompressible porous media equation
Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
The Euler equations as a differential inclusion
Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
A proof of Onsager's conjecture
Hölder continuous solutions of active scalar equations
Nonuniqueness of weak solutions to the Navier-Stokes equation
Nonlinear maximum principles for dissipative linear nonlocal operators and applications
Non-uniqueness of steady-state weak solutions to the surface quasi-geostrophic equations
Localized mixing zone for Muskat bubbles and turned interfaces
Mixing solutions for the Muskat problem
Anomalous dissipation for \(1/5\)-Hölder Euler flows
Existence and regularity of weak solutions to the quasi-geostrophic equations in the spaces \(L^p\) or \(\dot{H}^{-1/2}\)
Dissipative Euler Flows with Onsager-Critical Spatial Regularity
On the ill/well-posedness and nonlinear instability of the magneto-geostrophic equations
Convex integration for a class of active scalar equations
Analytical behavior of two-dimensional incompressible flow in porous media
Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
Relaxation of the incompressible porous media equation
On the supercritically diffusive magnetogeostrophic equations
A direct approach to nonuniqueness and failure of compactness for the SQG equation
Nonuniqueness of Weak Solutions to the SQG Equation
Magnetostrophic Turbulence and the Geodynamo
Nonuniqueness of Leray–Hopf solutions for a dyadic model