Abstract
A solution formula of the Stokes problem in the half space \(\mathbb {R}^{3}_{+}\) is obtained by focusing on the normal derivative of the pressure at the boundary. This explicit formula can be used to estimate the \(L^\infty \) norm of the pressure and its normal derivative at the boundary that quantifies the initial layer depending on regularity and compatibility conditions of the initial data.
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EAT acknowledges the support of the Institute of Mathematics and its Applications in the form of the a New Professor Fellowship for the year 2012–2013.
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Kim, H., Thomann, E.A. & Guenther, R.B. A Representation of the Solution of the Stokes Equations in the Half Space \(\mathbb {R}^{3}_{+}\): Application to Spatial and Temporal Estimates of the Pressure. J. Math. Fluid Mech. 21, 16 (2019). https://doi.org/10.1007/s00021-019-0419-4
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DOI: https://doi.org/10.1007/s00021-019-0419-4