Axi-symmetric solutions for active vector models generalizing 3D Euler and electron-MHD equations

DOI10.1016/j.nonrwa.2023.103953zbMath1529.35350arXiv2212.14515OpenAlexW4383336633MaRDI QIDQ6116288

Kyudong Choi, Donghao Chae, In-Jee Jeong

Publication date: 11 August 2023

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.14515

zbMATH Keywords

well-posednessEuler equationstraveling wavecommutator estimateHall equations

Mathematics Subject Classification ID

Magnetohydrodynamics and electrohydrodynamics (76W05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Traveling wave solutions (35C07) Euler equations (35Q31) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Axially symmetric solutions to PDEs (35B07)

Cites Work

• Unnamed Item
• Unnamed Item
• Fast growth of the vorticity gradient in symmetric smooth domains for 2D incompressible ideal flow
• Singularity formation for the incompressible Hall-MHD equations without resistivity
• Liouville type theorems for the steady axially symmetric Navier-Stokes and magnetohydrodynamic equations
• Finite time singularity for the modified SQG patch equation
• Nonlinear stability for steady vortex pairs
• Exponential growth of the vorticity gradient for the Euler equation on the torus
• Small scale creation for solutions of the incompressible two-dimensional Euler equation
• Infinite superlinear growth of the gradient for the two-dimensional Euler equation
• On the existence of global vortex rings
• Special issue editorial: Small scales and singularity formation in fluid dynamics
• Finite time blowup of 2D Boussinesq and 3D Euler equations with \(C^{1, \alpha}\) velocity and boundary
• Traveling vortex pairs for 2D incompressible Euler equations
• Vortex stretching and enhanced dissipation for the incompressible 3D Navier-Stokes equations
• The incompressible Euler equations under octahedral symmetry: singularity formation in a fundamental domain
• Finite-time singularity formation for \(C^{1,\alpha}\) solutions to the incompressible Euler equations on \(\mathbb{R}^3\)
• A single-component BKM-type regularity criterion for the inviscid axially symmetric Hall-MHD system
• Stability and instability of Kelvin waves
• Stability of monotone, nonnegative, and compactly supported vorticities in the half cylinder and infinite perimeter growth for patches
• Infinite growth in vorticity gradient of compactly supported planar vorticity near Lamb dipole
• Existence of vortex rings in Beltrami flows
• On the global classical solutions for the generalized SQG equation
• Stability of Lamb dipoles
• On the Cauchy problem for the Hall and electron magnetohydrodynamic equations without resistivity I: Illposedness near degenerate stationary solutions
• Compactness and stability for planar vortex-pairs with prescribed impulse
• Small scale creation in active scalars
• Growth of perimeter for vortex patches in a bulk
• The sharp corner formation in 2D Euler dynamics of patches: infinite double exponential rate of merging
• On the Cauchy problem for axi-symmetric vortex rings
• On the estimate of distance traveled by a particle in a disk-like vortex patch
• Finite-time singularity formation for strong solutions to the axi-symmetric \(3D\) Euler equations
• On vorticity gradient growth for the axisymmetric 3D Euler equations without swirl
• The centrally symmetric \(V\)-states for active scalar equations. two-dimensional Euler with cut-off
• Vorticity and Incompressible Flow
• A Simple Energy Pump for the Surface Quasi-geostrophic Equation
• Vortex Rings with Swirl: Axisymmetric Solutions of the Euler Equations with Nonzero Helicity
• Vortex Rings: Existence and Asymptotic Estimates
• Vortex-rings of prescribed impulse
• Existence and isoperimetric characterization of steady spherical vortex rings in a uniform flow in R^N
• Active vector models generalising 3D Euler and electron–MHD equations
• Asymptotic behaviour of global vortex rings
• On singular vortex patches, II: Long-time dynamics
• Symmetries and Critical Phenomena in Fluids
• Double exponential growth of the vorticity gradient for the two-dimensional Euler equation
• Filamentation near Hill’s vortex