Global well-posedness and quantitative flocking are shown for Lagrangian p-alignment dynamics; Eulerian variables are constructed via pushforward and disintegration, with defect terms vanishing asymptotically under heavy-tailed kernels to give mono-kinetic closure and mean-field convergence.
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A unified relative entropy framework yields quantitative strong and weak convergence for diffusive, high-field, and strong-magnetic-field limits of Vlasov-Fokker-Planck equations with Riesz-type interactions.
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Lagrangian formulation and Eulerian closure in alignment dynamics
Global well-posedness and quantitative flocking are shown for Lagrangian p-alignment dynamics; Eulerian variables are constructed via pushforward and disintegration, with defect terms vanishing asymptotically under heavy-tailed kernels to give mono-kinetic closure and mean-field convergence.
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A unified relative entropy framework for macroscopic limits of Vlasov--Fokker--Planck equations
A unified relative entropy framework yields quantitative strong and weak convergence for diffusive, high-field, and strong-magnetic-field limits of Vlasov-Fokker-Planck equations with Riesz-type interactions.