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.
Self-similar imploding solutions of the relativistic Euler equations
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2026 2verdicts
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Constructs self-similar blow-up solutions to axisymmetric Euler equations in d greater than or equal to 3 with initial data in C to the 1,alpha intersect smooth away from origin for alpha less than 1-2/d.
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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.
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Self-similar blow-up solutions of incompressible Euler equations in $\mathbb R^d, d\geq 3$ with $C^{1,1-2/d-}$ velocity
Constructs self-similar blow-up solutions to axisymmetric Euler equations in d greater than or equal to 3 with initial data in C to the 1,alpha intersect smooth away from origin for alpha less than 1-2/d.