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Award ID contains: 2304392

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  1. ; (, Communications in Mathematical Sciences)
    This paper explores the phenomena of enhanced dissipation in solutions to the passive scalar equations subject to time-dependent shear flows. The hypocoercivity functionals with carefully tuned time weights are applied in the analysis. We observe that as long as the critical points of the shear flow vary slowly, one can derive the sharp enhanced dissipation estimates, mirroring the ones obtained for the time-stationary case. 
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  2. (, SIAM Journal on Mathematical Analysis)
    In this paper, we investigate a coupled Patlak-Keller-Segel-Navier-Stokes (PKS-NS) system. We show that globally regular solutions with arbitrary large cell populations exist. The primary blowup suppression mechanism is the shear flow mixing induced enhanced dissipation phenomena. 
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  3. (, Journal of Functional Analysis)
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