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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3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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math.AP 3years
2026 3representative citing papers
For every d≥3 and every α<1−2/d, axisymmetric swirl-free incompressible Euler admits self-similar blow-up solutions with C^{1,α} initial velocity that is smooth away from the origin.
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.
citing papers explorer
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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 $d$-dimensional incompressible Euler equations with $C^{1,\left(1-2/d\right)-}$ velocity
For every d≥3 and every α<1−2/d, axisymmetric swirl-free incompressible Euler admits self-similar blow-up solutions with C^{1,α} initial velocity that is smooth away from the origin.
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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.