Periodic solutions for a 1D-model with nonlocal velocity via mass transport

DOI10.1016/j.jde.2016.01.018zbMath1339.35237arXiv1410.2905OpenAlexW2963912183MaRDI QIDQ264451

Lucas C. F. Ferreira, Julio C. Valencia-Guevara

Publication date: 31 March 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.2905

zbMATH Keywords

periodic solutionsfree energy functionalmass transportinviscid limitWasserstein distanceoptimal transportgradient flowsgeodesic with constant speednonlocal fluxes

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) PDEs in connection with fluid mechanics (35Q35) Periodic solutions to PDEs (35B10) Variational methods applied to PDEs (35A15) Initial value problems for second-order parabolic equations (35K15) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03)

Related Items (5)

On a 1D model with nonlocal interactions and mass concentrations: an analytical-numerical approach* ⋮ On the well-posedness via the JKO approach and a study of blow-up of solutions for a multispecies Keller-Segel chemotaxis system with no mass conservation ⋮ Singularity formation for the fractional Euler-alignment system in 1D ⋮ Well-posedness and critical thresholds in a nonlocal Euler system with relaxation ⋮ Minimizing movement for a fractional porous medium equation in a periodic setting

Cites Work

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• Second order stability for the Monge-Ampère equation and strong Sobolev convergence of optimal transport maps
• A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity
• Finite time singularities in a 1D model of the quasi-geostrophic equation
• Nonlinear diffusion of dislocation density and self-similar solutions
• Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations
• On a one-dimensional model for the three-dimensional vorticity equation
• Contractions in the 2-Wasserstein length space and thermalization of granular media
• Integral inequalities for the Hilbert transform applied to a nonlocal transport equation
• Global existence, singularities and ill-posedness for a nonlocal flux
• Well-posedness for a transport equation with nonlocal velocity
• Example of a displacement convex functional of first order
• Further properties of a continuum of model equations with globally defined flux
• A convexity principle for interacting gases
• Analytic structure of two 1D-transport equations with nonlocal fluxes
• \(W^{2,1}\) regularity for solutions of the Monge-Ampère equation
• Blow-up of solutions for a 1D transport equation with nonlocal velocity and supercritical dissipation
• Formation of singularities for a transport equation with nonlocal velocity
• On one-dimensional models for hydrodynamics
• Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• On a One-Dimensional Nonlocal Flux with Fractional Dissipation
• Sur le transport de mesures périodiques
• The Variational Formulation of the Fokker--Planck Equation
• A simple one‐dimensional model for the three‐dimensional vorticity equation
• Existence of Eulerian Solutions to the Semigeostrophic Equations in Physical Space: The 2-Dimensional Periodic Case
• Weak KAM Theory on the Wasserstein Torus with Multidimensional Underlying Space
• Polar factorization of maps on Riemannian manifolds

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