Constructs C^α self-similar blowup profiles for 3D Euler vorticity without swirl and proves asymptotically self-similar blowup from C_c^α data, with limiting factorization as α→(1/3)^-.
Nearly self-similar blowup of the slightly perturbed homogeneous Landau equation with very soft potentials.arXiv preprint arXiv:2311.11511, 2023
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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.
Derives a boundedness-based continuation criterion for the Landau-Coulomb equation that rules out Type II approximately self-similar blow-ups slower than Type I without decay assumptions on the inner profile.
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Asymptotically Self-Similar Blowup for 3D Incompressible Euler with $C^{1, 1/3-}$ Velocity II: 3D Profiles, Blowup, and Limiting behavior
Constructs C^α self-similar blowup profiles for 3D Euler vorticity without swirl and proves asymptotically self-similar blowup from C_c^α data, with limiting factorization as α→(1/3)^-.
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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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On Hydrodynamic Implosions and the Landau-Coulomb Equation
Derives a boundedness-based continuation criterion for the Landau-Coulomb equation that rules out Type II approximately self-similar blow-ups slower than Type I without decay assumptions on the inner profile.