Under a total mixing condition (the initial density ratio has bounded variation), global weak solutions exist for the two-species cross-diffusion system with independent drifts and no self-diffusion.
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On a Cross-Diffusion System with Independent Drifts and no Self-Diffusion: The Existence of Totally Mixed Solutions
Under a total mixing condition (the initial density ratio has bounded variation), global weak solutions exist for the two-species cross-diffusion system with independent drifts and no self-diffusion.