Lecture----数学院晨兴数学中心

Title:	Long time and small obstacle problem for the 2D Navier-Stokes equations
Speaker:	Professor Christophe Lacave (Université Grenoble Alpes)
Time:	2017-1-3, 16:30-17:30
Place:	410
Abstract:	We consider rigid bodies moving under the influence of a viscous fluid and we study the asymptotic as the size of the solids tends to zero. In a bounded domain, if the solids shrink to "massive" pointwise particles, we obtain a convergence to the solution of the Navier-Stokes equations independently to any possible collision of the bodies with the exterior boundary. In the case of "massless" pointwise particles, the energy equality is not sufficient anymore to derive a uniform estimate for the velocity of the solid. Our basic remark is that the small obstacle limit is related to the long-time behavior though the scaling property of the Navier-Stokes equations $u^\epsilon(t,x) = \epsilon^{-1} u^1 (\epsilon^{-2} t , \epsilon^{-1} x)$. Hence, we derive $L^p-L^q$ decay estimates for the linearized equations in the exterior of a unit disk. We then apply these estimates to treat the massless pointwise particle. (with S. Ervedoza, M. Hillairet and T. Takahashi)
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