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The gradient blow-up conjecture for local advection in multi-species models
Gradient blow-up conjecture. Failure to include non-locality in the advection term, equivalently setting $K$ to be a Dirac delta function, will lead to gradient blow-up.
Conjectureopenadvection-diffusion gradient-blow-up nonlocal-pdesarXiv posted 2 days ago

The gradient blow-up conjecture for local advection in multi-species models