Travelling and rotating solutions to the generalized inviscid surface quasi-geostrophic equation

DOI10.1090/tran/8406zbMath1477.35153arXiv2008.12911OpenAlexW3135776917MaRDI QIDQ5009320

Wei, Juncheng, Monica Musso, Juan Dávila, Weiwei Ao, Manuel A. del Pino

Publication date: 20 August 2021

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.12911

zbMATH Keywords

surface quasi-geostrophic equationfractional plasma equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) Singular perturbations in context of PDEs (35B25) Vortex flows for incompressible inviscid fluids (76B47) Fractional derivatives and integrals (26A33) Ionized gas flow in electromagnetic fields; plasmic flow (76X05) Semilinear elliptic equations (35J61) Traveling wave solutions (35C07) Fractional partial differential equations (35R11) PDEs in connection with geophysics (35Q86) Euler equations (35Q31) Geophysical flows (76U60)

Related Items (15)

On the global classical solutions for the generalized SQG equation ⋮ Multipole Vortex Patch Equilibria for Active Scalar Equations ⋮ Clustered travelling vortex rings to the axisymmetric three-dimensional incompressible Euler flows ⋮ Vortex collapses for the Euler and quasi-geostrophic models ⋮ Multiscale Steady Vortex Patches for 2D Incompressible Euler Equations ⋮ Co-rotating vortices with N fold symmetry for the inviscid surface quasi-geostrophic equation ⋮ Emergence of time periodic solutions for the generalized surface quasi-geostrophic equation in the disc ⋮ A note on the existence of stationary vortex patches for the SQG equation in bounded domain ⋮ Kármán vortex street for the generalized surface quasi-geostrophic equation ⋮ Well-posedness for SQG sharp fronts with unbounded curvature ⋮ Traveling waves near Couette flow for the 2D Euler equation ⋮ Desingularization of vortex rings in 3 dimensional Euler flows ⋮ Multiscale rotating vortex patches for 2D Euler flows in a disk ⋮ Existence and regularity of co-rotating and traveling-wave vortex solutions for the generalized SQG equation ⋮ Global solutions for the generalized SQG equation and rearrangements

Cites Work

• Finite time singularity for the modified SQG patch equation
• Relative equilibria in continuous stellar dynamics
• Desingularization of vortices for the Euler equation
• Euler evolution for singular initial data and vortex theory
• Fast and slow decay solutions for supercritical elliptic problems in exterior domains
• Asymptotic estimates for the plasma problem
• Measure of degenerate relative equilibria. I
• A non-linear eigenvalue problem: the shape at equilibrium of a confined plasma
• Classifying relative equilibria. III
• Asymptotic shape and location of small cores in elliptic free-boundary problems
• Ground states in the diffusion-dominated regime
• Uniqueness of entire ground states for the fractional plasma problem
• Gluing methods for vortex dynamics in Euler flows
• Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
• Regularization of point vortices pairs for the Euler equation in dimension two
• Desingularization of vortex rings and shallow water vortices by a semilinear elliptic problem
• Entire $s$-harmonic functions are affine
• Uniqueness of Radial Solutions for the Fractional Laplacian
• Generalized surface quasi-geostrophic equations with singular velocities
• Global Smooth Solutions for the Inviscid SQG Equation
• Regular Polygon Solutions of the N-Body Problem
• Classifying relative equilibria. II
• Remarks on a free Boundary Value Problem Arising in Plasma Physics
• Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
• Harmonic Radius and Concentration of Energy; Hyperbolic Radius and Liouville’s Equations $\Delta U = e^U $ and $\Delta U = U^{\tfrac{{n + 2}}{{n - 2}}} $
• Justification of the Point Vortex Approximation for Modified Surface Quasi-Geostrophic Equations
• ODE Methods in Non-Local Equations
• Multivortex Traveling Waves for the Gross--Pitaevskii Equation and the Adler--Moser Polynomials
• Classifying relative equilibria. I
• Local Regularity for the Modified SQG Patch Equation
• Smooth Travelling-Wave Solutions to the Inviscid Surface Quasi-Geostrophic Equation
• The Supercritical Lane–Emden–Fowler Equation in Exterior Domains
• An Extension Problem Related to the Fractional Laplacian

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