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Creators/Authors contains: "He, Siming"

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  1. ; ; ; (, Journal of Functional Analysis)
    Free, publicly-accessible full text available October 1, 2026
  2. ; (, SIAM Journal on Mathematical Analysis)
    Free, publicly-accessible full text available August 31, 2026
  3. (, Journal of Functional Analysis)
    We consider the three-dimensional parabolic-parabolic Patlak-Keller-Segel equations (PKS) subject to ambient flows. Without the ambient fluid flow, the equation is super-critical in three-dimension and has finite-time blow-up solutions with arbitrarily small $L^1$-mass. In this study, we show that a family of time-dependent alternating shear flows, inspired by the clever ideas of Tarek Elgindi [39], can suppress the chemotactic blow-up in these systems. 
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    Free, publicly-accessible full text available March 1, 2026
  4. (, Nonlinearity)
    Abstract In this study, we investigate the behavior of three-dimensional parabolic–parabolic Patlak–Keller–Segel systems in the presence of ambient shear flows. Our findings demonstrate that when the total mass of the cell density is below a specific threshold, the solution remains globally regular as long as the flow is sufficiently strong. The primary difficulty in our analysis stems from the fast creation of chemical gradients due to strong shear advection. 
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  5. ; ; ; (, Communications in Mathematical Physics)
    Free, publicly-accessible full text available February 1, 2026
  6. ; (, 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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  7. (, 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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  8. ; (, Nonlinearity)
    Abstract We consider absorbing chemical reactions in a fluid flow modelled by the coupled advection–reaction–diffusion equations. In these systems, the interplay between chemical diffusion and fluid transportation causes the enhanced dissipation phenomenon. We show that the enhanced dissipation time scale, together with the reaction coupling strength, determines the characteristic time scale of the reaction. 
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  9. ; ; (, Communications of the American Mathematical Society)
    We study two types of divergence-free fluid flows on unbounded domains in two and three dimensions—hyperbolic and shear flows—and their influence on chemotaxis and combustion. We show that fast spreading by these flows, when they are strong enough, can suppress growth of solutions to PDE modeling these phenomena. This includes prevention of singularity formation and global regularity of solutions to advective Patlak-Keller-Segel equations on R 2 \mathbb {R}^2 and R 3 \mathbb {R}^3 , confirming numerical observations by Khan, Johnson, Cartee, and Yao [Involve 9 (2016), pp. 119–131], as well as quenching in advection-reaction-diffusion equations. 
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  10. ; ; (, Bulletin of Mathematical Biology)
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