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In this paper, we investigate nonlocal interaction equations with repulsive-attractive radial potentials.
Dynamics of vortex liquids in ginzburg-landau theories with applications to superconductivity
E. Weinan · 1994
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A kinetic a kinetic equation for granular media
M. Pulvirenti D. Benedetto, E. Caglioti · 1997
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An integrodifferential model for orientational distributions of f-actin in cells
E. Geigant, K. Ladizhansky, and A. Mogilner · 1998
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A non-local model for a swarm
A. Mogilner and L. Edelstein-Keshet · 1999
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On the hydrodynamic limit of ginzburg-landau vortices
F. Lin and P. Zhang · 2000
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A rigorous derivation of a free-boundary problem arising in superconductivity
E. Sandier and S. Serfaty · 2000
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One-dimensional kinetic models of granular flows
G. Toscani · 2000
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High-field limit for the Vlasov-Poisson-Fokker-Planck system
J. Nieto, F. Poupaud, and J. Soler · 2001
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Diffusion and Ecological Problems
A. Okubo and Levin S.A · 2001
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Properly embedded minimal surfaces with finite total curvature
Joaquín Pérez and Antonio Ros · 2002
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Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
J. A. Carrillo, R. J. McCann, and C. Villani · 2003
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Existence of weak solutions to some vortex density models
Q. Du and P. Zhang · 2003
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Mutual interactions, potentials, and individual distance in a social aggregation
A. Mogilner, L. Edelstein-Keshet, L. Bent, and A. Spiros · 2003
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Topics in optimal transportation
C. Villani · 2003
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Finite speed of propagation in porous media by mass transportation methods
J. A. Carrillo, M. P. Gualdani, and G. Toscani · 2004
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Optimal critical mass in the two-dimensional Keller-Segel model in ℝ 2 \mathbb{R}^{2}
J. Dolbeault and B. Perthame · 2004
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Long-time asymptotics of kinetic models of granular flows
H. Li and G. Toscani · 2004
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Swarming patterns in a two-dimensional kinematic model for biological groups
C. M. Topaz and A. L. Bertozzi · 2004
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Gradient flows in metric spaces and in the space of probability measures
L. A. Ambrosio, N. Gigli, and G. Savarè · 2005
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Global solutions to vortex density equations arising from sup-conductivity
N. Masmoudi and P. Zhang · 2005
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Two-dimensional Keller-Segel model: optimal critical mass and qualitative properties of the solutions
A. Blanchet, J. Dolbeault, and B. Perthame · 2006
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Contractions in the 2-Wasserstein length space and thermalization of granular media
J. A. Carrillo, R. J. McCann, and C. Villani · 2006
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Lagrangian numerical approximations to one-dimensional convolution-diffusion equations
L. Gosse and G. Toscani · 2006
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Stable rotating binary stars and fluid in a tube
R. J. McCann · 2006
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A nonlocal continuum model for biological aggregation
C. M. Topaz, A. L. Bertozzi, and M. A. Lewis · 2006
Numerical simulation of diffusive and aggregation phenomena in nonlinear continuity equations by evolving diffeomorphisms
J. A. Carrillo and J. S. Moll · 2009
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Double milling in self-propelled swarms from kinetic theory
J.A. Carrillo, M.R. D’Orsogna, and V. Panferov · 2009
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An integro-differential equation model for alignment and orientational aggregation
K. Kang, B. Perthame, A. Stevens, and J.J.L. Velazquez · 2009
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A global uniqueness result for an evolution problem arising in superconductivity
E. Mainini · 2009
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Mass-selection in alignment models with non-deterministic effects
I. Primi, A. Stevens, and J. J.L. Velazquez · 2009
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Gradient flow of the chapman-rubinstein-schatzman model for signed vortices
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Finite-time blow-up of solutions of an aggregation equation in ℝ n \mathbb{R}^{n}
A. Bertozzi and T. Laurent · 2007
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An ODE model of the motion of pelagic fish
B. Birnir · 2007
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Emergent behavior in flocks
F. Cucker and S. Smale · 2007
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On the mathematics of emergence
F. Cucker and S. Smale · 2007
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Local and global existence for an aggregation equation
T. Laurent · 2007
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Vortices in the magnetic Ginzburg-Landau model
E. Sandier and S. Serfaty · 2007
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L. Ambrosio, E. Mainini, and S. Serfaty · 2010
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Finite-time blow-up of l ∞ l^{\infty} -weak solutions of an aggregation equation
A. Bertozzi and J. Brandman · 2010
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Uniqueness of bounded solutions to aggregation equations by optimal transport methods
J. A. Carrillo and J. Rosado · 2010
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Asymptotic flocking dynamics for the kinetic cucker-smale model
J.A. Carrillo, M. Fornasier, J. Rosado, and G. Toscani · 2010
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Stable stationary states of non-local interaction equations
K. Fellner and G. Raoul · 2010
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Non-local interaction equations: Stationary states and stability analysis
G. Raoul · 2010
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Lp theory for the multidimensional aggregation equation
A. Bertozzi, T. Laurent, and J. Rosado · 2011
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A well-posedness theory in measures for some kinetic models of collective motion
J.A. Cañizo, J.A. Carrillo, and J. Rosado · 2011
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Confinement in nonlocal interaction equations
J. A. Carrillo, M. Di Francesco, A. Figalli, T. Laurent, and D. Slepčev · 2011
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Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations
J. A. Carrillo, M. Di Francesco, A. Figalli, T. Laurent, and D. Slepčev · 2011
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The aggregation equation with power-law kernels: ill-posedness, mass concentration and similarity solutions
H. Dong · 2011
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Swarm dynamics and equilibria for a nonlocal aggregation model
R. C. Fetecau, Y. Huang, and T. Kolokolnikov · 2011
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Stability of ring patterns arising from 2d particle interactions
T. Kolokonikov, H. Sun, D. Uminsky, and A. Bertozzi · 2011
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