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Reacting Multi-component Fluids: Regular Solutions in Lorentz Spaces

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Abstract

The paper deals with the analysis of a model of a multi-component fluid admitting chemical reactions. The flow is considered in the incompressible regime. The main result shows the global existence of regular solutions under the assumption of suitable smallness conditions. In order to control the solutions a special structure condition on the derivatives of chemical production functions determining the reactions is required. The existence is shown in a new critical functional framework of Lorentz spaces of type \(L_{p,r}(0,T;L_q)\), which allows to control the integral \(\int _0^\infty \Vert \nabla u(t)\Vert _{\infty } dt\).

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Acknowledgements

The authors have been partially supported by National Science Centre Grant No2018/29/B/ST1/00339 (Opus). The authors would also like to thank the anonymous Referees who pointed out several important points in the first version of the manuscript. Their careful lecture of the manuscript contributed a lot to the quality of the paper.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Piotr Bogusław Mucha & Tomasz Piasecki

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  1. Piotr Bogusław Mucha
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  2. Tomasz Piasecki
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Correspondence to Piotr Bogusław Mucha.

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Communicated by T. Ozawa.

Dedicated to Professor Yoshihiro Shibata on occasion of his 70th anniversary.

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This article is part of the topical collection “Yoshihiro Shibata”.

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Mucha, P.B., Piasecki, T. Reacting Multi-component Fluids: Regular Solutions in Lorentz Spaces. J. Math. Fluid Mech. 24, 37 (2022). https://doi.org/10.1007/s00021-022-00670-x

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