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Title: | On some mixed-transmission problems for the anisotropic Stokes and Navier-Stokes systems in Lipschitz domains with transversal interfaces |
Authors: | Mikhailov, S Wendland, WL |
Keywords: | Anisotropic Stokes and Navier-Stokes systems with L ∞ coefficients;variational approach;L 2 -based Sobolev spaces;mixed and mixed-transmission problems;existence and uniqueness results;fixed point theorem 2000 MSC: 35J57, 35Q30, 46E35, 76D, 76M |
Issue Date: | 2022 |
Publisher: | Journal of Mathematical Analysis and Applications |
Citation: | Kohr. M., Mikhailov. S., Wendland. W.L. (2022) 'On some mixed-transmission problems for the anisotropic Stokes and Navier-Stokes systems in Lipschitz domains with transversal interfaces', Journal of Mathematical Analysis and Aplication, 0, pp.1 - 24. doi: |
Abstract: | The main purpose of this paper is the analysis of mixed-transmission problems for the anisotropic Stokes system in a compressible framework and in bounded Lipschitz domains with transversal Lipschitz interfaces in Rn, n ≥ 2. Mixed problems and mixed-transmission problems for the anisotropic Navier-Stokes system in dimension n ∈ {2, 3} are also considered. The anisotropy is highlighted by an L∞-viscosity tensor coefficient, which satisfies an ellipticity condition in terms of symmetric matrices in Rn×n with null traces. In the first part we use a variational approach to show the well-posedness of the analyzed linear problems for the Stokes system in L2-based Sobolev spaces. In the second part we show the existence and uniqueness of a weak solution of the mixed problem for the anisotropic compressible Navier-Stokes system with small data in L2-based Sobolev spaces in a bounded Lipschitz domain in Rn, n ∈ {2, 3}. A mixed-transmission problem for the Navier-Stokes system in a Lipschitz domain with a transversal Lipschitz interface is also considered. |
URI: | http://bura.brunel.ac.uk/handle/2438/24796 |
ISSN: | 0022-247X |
Appears in Collections: | Dept of Mathematics Embargoed Research Papers |
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