Global existence of weak solutions is established for 1D cross-diffusion systems with arbitrary advections via vanishing-viscosity limit and a three-entropy compensated-compactness argument that exploits oscillation correlation.
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Mean-field SVGD flow converges locally at explicit polynomial L2 rates to the target on the torus for Riesz kernels, with rates depending on dimension and regularity, sharpness in some regimes, and recovery of global exponential convergence for Coulomb kernels.
SVGD dynamics with concentrating kernels converge to a local Wasserstein gradient flow with quadratic mobility.
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Global solutions to cross-diffusion systems with independent advections in one dimension
Global existence of weak solutions is established for 1D cross-diffusion systems with arbitrary advections via vanishing-viscosity limit and a three-entropy compensated-compactness argument that exploits oscillation correlation.
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Quantitative Local Convergence of Mean-Field Stein Variational Gradient Flow
Mean-field SVGD flow converges locally at explicit polynomial L2 rates to the target on the torus for Riesz kernels, with rates depending on dimension and regularity, sharpness in some regimes, and recovery of global exponential convergence for Coulomb kernels.
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Stein Variational Gradient Descent dynamics for highly concentrated kernels
SVGD dynamics with concentrating kernels converge to a local Wasserstein gradient flow with quadratic mobility.