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.
Nonuniquene ss of leray-hopf solutions to the unforced incom- pressible 3d navier-stokes equation
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Constructs C^∞ self-similar blowup profiles for 1D models of 3D Euler at α=1/3 using fixed-point around a numerical approximation, plus nearby exact profiles for α slightly below 1/3.
The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.
Theorems on uniqueness and continuous dependence on initial data for stochastic Navier-Stokes equations with Wiener and Poisson noise, generalizing results from GK2026.
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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.
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Asymptotically Self-Similar Blowup for 3D Incompressible Euler with $C^{1, 1/3-}$ Velocity I: $C^{\infty}$ 1D Limiting Profiles
Constructs C^∞ self-similar blowup profiles for 1D models of 3D Euler at α=1/3 using fixed-point around a numerical approximation, plus nearby exact profiles for α slightly below 1/3.
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Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches
The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.
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On uniqueness of solutions to stochastic Navier--Stokes equations
Theorems on uniqueness and continuous dependence on initial data for stochastic Navier-Stokes equations with Wiener and Poisson noise, generalizing results from GK2026.