New smooth self-similar implosion profiles for compressible Euler equations are constructed with explicit exponents and proven stable under radial and certain non-radial perturbations.
On blow up for the energy super critical defocusing nonlinear Schr¨odinger equations.Invent
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Smooth and stable Euler implosions
New smooth self-similar implosion profiles for compressible Euler equations are constructed with explicit exponents and proven stable under radial and certain non-radial perturbations.