4 problems

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Uniform boundedness conjecture for subcritical-mass Patlak–Keller–Segel–Navier–Stokes solutions
Uniform boundedness conjecture. If $M<8\pi$ , then the solutions are uniformly bounded in time.
Conjectureopencritical-mass navier-stokes patlak-keller-segelarXiv posted 2 days ago
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Finite-time blow-up conjecture for the multi-species Patlak–Keller–Segel system
Let $\mathbf{B}$ be a symmetric matrix with positive entries, and let $\mathbf{M}$ , $\mathcal{I}$ , $Q_{\mathbf{B},\mathbf{M}}$ , and $\operatorname{supp}(\mathbf{B})$ be as in the p…
Conjectureopenblow-up multi-species-systems patlak-keller-segelarXiv posted 2 days ago
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Critical-parameter conjecture for the higher-dimensional Patlak–Keller–Segel gradient flow
In the higher-dimensional setting, let $\alpha$ be the parameter in the driving functional governing the equation. For $\alpha=1$ , this functional is precisely the one that is non-…
Conjectureopengradient-flows hardy-littlewood-sobolev-inequality patlak-keller-segelarXiv posted 2 days ago
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The critical-mass aggregation conjecture for the two-dimensional parabolic-elliptic Patlak–Keller–Segel system
Consider the two-dimensional parabolic-elliptic Patlak–Keller–Segel system … with nonnegative initial density $\rho_0$ and conserved mass … Here $\rho$ is the cell density,…
Conjectureopenaggregation chemotaxis patlak-keller-segelarXiv posted 2 days ago

4 problems

Uniform boundedness conjecture for subcritical-mass Patlak–Keller–Segel–Navier–Stokes solutions

Finite-time blow-up conjecture for the multi-species Patlak–Keller–Segel system

Critical-parameter conjecture for the higher-dimensional Patlak–Keller–Segel gradient flow

The critical-mass aggregation conjecture for the two-dimensional parabolic-elliptic Patlak–Keller–Segel system