The Green tensor of the nonstationary Stokes system in the half space

Abstract: We prove the first-ever pointwise estimates of the (unrestricted) Green tensor and the associated pressure tensor of the nonstationary Stokes system in the half-space, for every space dimension greater than one. The force field is not necessarily assumed to be solenoidal. The key is to find a suitable Green tensor formula that maximizes the tangential decay, showing in particular the integrability of Green tensor derivatives. With its pointwise estimates, we show the symmetry of the Green tensor, which in turn improves pointwise estimates. We also study how the solutions converge to the initial data, and the (infinitely many) restricted Green tensors acting on solenoidal vector fields. As applications, we give new proofs of the existence of mild solutions of the Navier-Stokes equations in Lq, pointwise decay, and uniformly local Lq spaces in the half-space. This talk is based on arXiv:2011.00134, a joint work with Kyungkeun Kang, Baishun Lai and Chen-Chih Lai.

MathematicsPhysics

Audience: researchers in the topic

Comments: This seminar session will exceptionally start at 16:30.

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Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).

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