For a broad class of nonlinear parabolic PDEs, adding an incompressible drift with sufficiently small dissipation time ensures global boundedness and exponential decay, including Keller-Segel blow-up prevention and reaction quenching by simple cellular flows.
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Convection-Induced Singularity Suppression in the Keller-Segel and Other Non-linear PDEs
For a broad class of nonlinear parabolic PDEs, adding an incompressible drift with sufficiently small dissipation time ensures global boundedness and exponential decay, including Keller-Segel blow-up prevention and reaction quenching by simple cellular flows.