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arXiv · 1903.03832

Green functions for pressure of Stokes systems

Jongkeun Choi·Hongjie Dong
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Abstract

We study Green functions for the pressure of stationary Stokes systems in a (possibly unbounded) domain $\Omega\subset \mathbb{R}^d$, where $d\ge 2$. We construct the Green function when coefficients are merely measurable in one direction and have Dini mean oscillation in the other directions, and $\Omega$ is such that the divergence equation is solvable there. We also establish global pointwise bounds for the Green function and its derivatives when coefficients have Dini mean oscillation and $\Omega$ has a $C^{1,\rm{Dini}}$ boundary. Green functions for the flow velocity of Stokes systems are also considered.

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Jongkeun Choi, Hongjie Dong. 2019-03-09. Green functions for pressure of Stokes systems. https://arxiv.org/abs/1903.03832

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