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Classical solutions of the Robin problem for the Darcy-Forchheimer-Brinkman system

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Abstract

We study classical solutions of the Robin problem for the Brinkman system and for the Darcy-Forchheimer-Brinkman system in a bounded domain with Lyapunov boundary. First we prove unique solvability of the Robin problem for the Brinkman system in the function space \(\left[ {{\mathcal {C}}}^{1,\beta } ({\overline{\Omega }} ;{\mathbb R}^m)\cap {{\mathcal {C}}}^2 (\Omega ;{\mathbb R}^m)\right] \times \left[ {{\mathcal {C}}}^\beta ({\overline{\Omega }} )\cap {\mathcal {C}}^1 (\Omega )\right] \). Then we show the existence of a solution of the Robin problem for the Darcy-Forchheimer-Brinkman system in the same space for sufficiently small data.

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  1. Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 115 67, Praha 1, Czech Republic

    Dagmar Medková

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Medková, D. Classical solutions of the Robin problem for the Darcy-Forchheimer-Brinkman system. Z. Angew. Math. Phys. 72, 44 (2021). https://doi.org/10.1007/s00033-021-01479-w

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