Constructs C^α self-similar blowup profiles for 3D Euler vorticity without swirl and proves asymptotically self-similar blowup from C_c^α data, with limiting factorization as α→(1/3)^-.
Vorticity blowup in 2D compressible Euler equations
5 Pith papers cite this work. Polarity classification is still indexing.
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math.AP 5years
2026 5representative citing papers
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.
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.
Constructs smooth initial data for isentropic compressible Euler equations in R^2 and R^3 such that solutions exhibit arbitrarily large localized velocity and pressure gradients near prescribed points while remaining C^1-smooth and bounded elsewhere.
citing papers explorer
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Asymptotically Self-Similar Blowup for 3D Incompressible Euler with $C^{1, 1/3-}$ Velocity II: 3D Profiles, Blowup, and Limiting behavior
Constructs C^α self-similar blowup profiles for 3D Euler vorticity without swirl and proves asymptotically self-similar blowup from C_c^α data, with limiting factorization as α→(1/3)^-.
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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.
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Formation of quasi-singularities of shock and implosion type for compressible Euler flows
Constructs smooth initial data for isentropic compressible Euler equations in R^2 and R^3 such that solutions exhibit arbitrarily large localized velocity and pressure gradients near prescribed points while remaining C^1-smooth and bounded elsewhere.