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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17 Pith papers cite this work. Polarity classification is still indexing.
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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.
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.
Computer-assisted construction of a finite-time singularity for 3D incompressible Navier-Stokes on T^3 via a 5D-lifted analytic profile and periodic extension.
Numerical construction of unstable self-similar axially symmetric swirl-free solutions to the incompressible Navier-Stokes equations on R^3 with global pointwise residuals of order 10^{-10}.
Introduces a matrix-clock criterion and reduces it to a scalar clock inequality that rules out finite-time collapse of the deformation gradient for conditional C^{1,α} axisymmetric Euler solutions when α ≥ 1/3.
Pseudo-transport noise with tunable small-scale parameter a delays blow-up in 3D Euler and Navier-Stokes equations with high probability.
Computer-assisted proof shows that the linearized operator around threefold symmetric traveling waves in the Burgers-Hilbert equation has an eigenvalue with negative real part for ω=3 and c≈1.1.
The authors unify the Boussinesq and axisymmetric Euler systems into a parameterized boundary-jet model and prove finite-time blow-up for its closed truncation using a Riccati argument.
Smooth initial data for 1D compressible Euler with vacuum boundary can develop gradient blowup at the boundary in finite time.
A coefficient-based unification of two fluid equations yields exact (1+1)D reductions whose apex dynamics blow up in finite time under stated conditional stability assumptions.
Proves W^{1,∞} stability for 1D hyperbolic conservation laws with inflow data and W^{2,3+} stability for a large class of shear flows in the 3D Euler system with inflow BC in pipes.
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.
G-invariant divergence-free initial data on compact cohomogeneity-one manifolds yield global smooth G-invariant solutions to the incompressible Euler equations.
Proves improved lower bounds on vorticity growth for generalized anti-parallel vortex tube solutions to the Euler equations in dimensions n ≥ 3.
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 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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Stable Finite-Time Singularity Formation for 3D Navier--Stokes via 5D-Lifted Axisymmetric Reductions
Computer-assisted construction of a finite-time singularity for 3D incompressible Navier-Stokes on T^3 via a 5D-lifted analytic profile and periodic extension.
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On the non-uniqueness of solutions of the axi-symmetric swirl-free Navier-Stokes equations, I
Numerical construction of unstable self-similar axially symmetric swirl-free solutions to the incompressible Navier-Stokes equations on R^3 with global pointwise residuals of order 10^{-10}.
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A conditional Lagrangian clock barrier at the $C^{1,\frac{1}{3}}$ threshold for axisymmetric Euler without swirl
Introduces a matrix-clock criterion and reduces it to a scalar clock inequality that rules out finite-time collapse of the deformation gradient for conditional C^{1,α} axisymmetric Euler solutions when α ≥ 1/3.
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Delayed Blow-up in 3D Fluids via Pseudo-transport Noise
Pseudo-transport noise with tunable small-scale parameter a delays blow-up in 3D Euler and Navier-Stokes equations with high probability.
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Linear instability of a Burgers--Hilbert traveling wave
Computer-assisted proof shows that the linearized operator around threefold symmetric traveling waves in the Burgers-Hilbert equation has an eigenvalue with negative real part for ω=3 and c≈1.1.
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A unified Boussinesq--Euler formulation and finite-time blow-up for a Hou--Luo type boundary-jet system
The authors unify the Boussinesq and axisymmetric Euler systems into a parameterized boundary-jet model and prove finite-time blow-up for its closed truncation using a Riccati argument.
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Gradient blowup of smooth vacuum solutions to 1D compressible Euler equations
Smooth initial data for 1D compressible Euler with vacuum boundary can develop gradient blowup at the boundary in finite time.
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2D inviscid Boussinesq equations and 3D axisymmetric Euler equations: (1) A unification ($Em$), (2) Finite-time blow-up of two unified $(1+1)$D systems rigorously derived from ($Em$)
A coefficient-based unification of two fluid equations yields exact (1+1)D reductions whose apex dynamics blow up in finite time under stated conditional stability assumptions.
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Stability of Inflow Problem for Hyperbolic Systems
Proves W^{1,∞} stability for 1D hyperbolic conservation laws with inflow data and W^{2,3+} stability for a large class of shear flows in the 3D Euler system with inflow BC in pipes.
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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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Incompressible Euler fluids on compact cohomogeneity one manifolds
G-invariant divergence-free initial data on compact cohomogeneity-one manifolds yield global smooth G-invariant solutions to the incompressible Euler equations.
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Growth rates for anti-parallel vortex tube Euler flows in three and higher dimensions
Proves improved lower bounds on vorticity growth for generalized anti-parallel vortex tube solutions to the Euler equations in dimensions n ≥ 3.
- Incompressible Euler Blowup at the $C^{1,\frac{1}{3}}$ Threshold