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.
Self-similar singular solutions to the nonlinear Schr¨ odinger and the Comp lex Ginzburg-Landau equations
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The parabolic-elliptic Keller-Segel system is locally ill-posed in L^q(R^n) for n=3..9 and supercritical q in [1, n/2).
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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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Spectral instability and non-uniqueness of mild solutions for the Keller-Segel system
The parabolic-elliptic Keller-Segel system is locally ill-posed in L^q(R^n) for n=3..9 and supercritical q in [1, n/2).