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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6 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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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.
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.
Finite-time vorticity blow-up is shown to exist for the forced 2D non-homogeneous Euler equations via adaptation of a prior Boussinesq construction.
The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.
A simpler proof of Vishik's nonuniqueness theorem for the forced 2D Euler equation is obtained by constructing an unstable vortex first as piecewise constant and then regularizing it via a fixed-point argument.
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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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.
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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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Vorticity blow-up for the 2D incompressible non-homogeneous Euler equations with uniform $C^{1,\sqrt{\frac{4}{3}}-1-\varepsilon}$ force
Finite-time vorticity blow-up is shown to exist for the forced 2D non-homogeneous Euler equations via adaptation of a prior Boussinesq construction.
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Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches
The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.
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A proof of Vishik's nonuniqueness Theorem for the forced 2D Euler equation
A simpler proof of Vishik's nonuniqueness theorem for the forced 2D Euler equation is obtained by constructing an unstable vortex first as piecewise constant and then regularizing it via a fixed-point argument.