For n=3,...,9 and every q<n/2, the parabolic–elliptic Keller–Segel system admits two distinct mild L^q solutions with the same initial condition.
Self-similar singular solutions to the nonlinear Schr¨ odinger and the Comp lex Ginzburg-Landau equations
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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.
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Spectral instability and non-uniqueness for the Keller-Segel system
For n=3,...,9 and every q<n/2, the parabolic–elliptic Keller–Segel system admits two distinct mild L^q solutions with the same initial condition.
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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.