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A Dirichlet-Transmission Problem for Darcy–Forchheimer–Brinkman and Navier–Stokes Equations in Bounded Lipschitz Domain

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Abstract

A boundary value problem of Dirichlet-transmission type for the nonlinear Darcy–Forchheimer–Brinkman and Navier–Stokes equations in two adjacent bounded Lipschitz domains from \(\mathbb {R}^{3}\) has been studied. The existence and uniqueness of a weak solution in some Sobolev spaces is obtained using a layer potential approach and a fixed point theorem, when the boundary data are chosen in some \(L^{2}\)-based Sobolev spaces and are suitable small.

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Notes

  1. \(C^{\infty }_{\textrm{comp}}\left( \mathbb {R}^{3}, \mathbb {R}^{3}\right) \) is the space of infinitely differentiable vector-valued functions with compact support in \(\mathbb {R}^{3}\), endowed with the inductive limit topology (cf. e.g. [13]).

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  1. Faculty of Mathematics and Computer Science, Babes-Bolyai University, 1 M. Kogalniceanu street, 400084, Cluj-Napoca, Romania

    Ioan Papuc

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Papuc, I. A Dirichlet-Transmission Problem for Darcy–Forchheimer–Brinkman and Navier–Stokes Equations in Bounded Lipschitz Domain. Results Math 79, 55 (2024). https://doi.org/10.1007/s00025-023-02081-4

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