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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2026 2representative citing papers
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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Stein Variational Gradient Descent dynamics for highly concentrated kernels
SVGD dynamics with concentrating kernels converge to a local Wasserstein gradient flow with quadratic mobility.