Vorticity gradients for the Euler equation on the sphere are bounded above by double-exponential growth in time, with this rate achieved by explicit symmetric constructions.
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6 Pith papers cite this work. Polarity classification is still indexing.
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Linear stability analysis of the Lamb-Chaplygin dipole fully classifies the spectrum and Jordan chains, showing growth only through two explicit mechanisms tied to circulation and zero-eigenvalue chains.
The 2D anisotropic Navier-Stokes equations with horizontal fractional dissipation of order 2s are globally stable with algebraic decay for all 0 ≤ s < 1.
In the odd symmetric half-plane setting, every compactly supported nonnegative initial vorticity admits an arbitrarily small smooth nonnegative perturbation that forces linear-in-time filamentation for the 2D Euler flow.
Initial data is constructed for 2D gravity-capillary water waves with vorticity in an unbounded domain such that the L^∞ norm of the vorticity gradient grows at least double-exponentially during the solution lifespan.
Spectral stability of the Lamb-Chaplygin dipole holds for the 2D Euler equation without symmetry conditions, with linear fluctuation bounds and velocity control under symmetry.
citing papers explorer
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Growth of vorticity gradient for the Euler equation on the sphere
Vorticity gradients for the Euler equation on the sphere are bounded above by double-exponential growth in time, with this rate achieved by explicit symmetric constructions.
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Linear Stability of the Lamb-Chaplygin Dipole
Linear stability analysis of the Lamb-Chaplygin dipole fully classifies the spectrum and Jordan chains, showing growth only through two explicit mechanisms tied to circulation and zero-eigenvalue chains.
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Stability and Decay for the 2D Anisotropic Navier-Stokes Equations with Fractional Horizontal Dissipation on $\mathbb{R}^2$
The 2D anisotropic Navier-Stokes equations with horizontal fractional dissipation of order 2s are globally stable with algebraic decay for all 0 ≤ s < 1.
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Remarks on Linear Growth of Vorticity Gradients and Support Diameters for 2D Euler Flow in Half-Plane
In the odd symmetric half-plane setting, every compactly supported nonnegative initial vorticity admits an arbitrarily small smooth nonnegative perturbation that forces linear-in-time filamentation for the 2D Euler flow.
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Small scale creation in 2D gravity-capillary water waves with vorticity
Initial data is constructed for 2D gravity-capillary water waves with vorticity in an unbounded domain such that the L^∞ norm of the vorticity gradient grows at least double-exponentially during the solution lifespan.
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On the stability of Lamb-Chaplygin dipole for the 2D Euler equation
Spectral stability of the Lamb-Chaplygin dipole holds for the 2D Euler equation without symmetry conditions, with linear fluctuation bounds and velocity control under symmetry.