Weak solutions to 2D viscous resistive MHD are non-unique in L^2_t L^p(R^2) ∩ L^1_t W^{1,p}(R^2) for all 1 ≤ p < ∞, with byproducts for Navier-Stokes and large BMO^{-1} data.
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Constructs divergence-free drifts in C_t L^{d-} yielding infinitely many distinct solutions to nonlinear Fokker-Planck equations and at least N distinct stationary martingale solutions to DDSDEs for any N when d≥3.
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Sharp non-uniqueness of weak solutions to 2D magnetohydrodynamic equations
Weak solutions to 2D viscous resistive MHD are non-unique in L^2_t L^p(R^2) ∩ L^1_t W^{1,p}(R^2) for all 1 ≤ p < ∞, with byproducts for Navier-Stokes and large BMO^{-1} data.