Piasecki, T;
Shibata, Y;
Zatorska, E;
(2019)
On strong dynamics of compressible two-component mixture flow.
SIAM Journal on Mathematical Analysis
, 51
(4)
pp. 2793-2849.
10.1137/17M1151134.
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Abstract
We investigate a system describing the flow of a compressible two-component mixture. The system is composed of the compressible Navier–Stokes equations coupled with nonsymmetric reaction-diffusion equations describing the evolution of fractional masses. We show the local existence and, under certain smallness assumptions, also the global existence of unique strong solutions in an Lp-Lq framework. Our approach is based on so-called entropic variables which enable us to rewrite the system in a symmetric form. Then, applying Lagrangian coordinates, we show the local existence of solutions applying the Lp-Lq maximal regularity estimate. Next, applying an exponential decay estimate we show that the solution exists globally in time provided the initial data is sufficiently close to some constants. The nonlinear estimates impose restrictions 2 <p< ∞, 3 <q< ∞. However, for the purpose of generality, we show the linear estimates for a wider range of p and q.
| Type: | Article |
|---|---|
| Title: | On strong dynamics of compressible two-component mixture flow |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/17M1151134 |
| Publisher version: | http://doi.org/10.1137/17M1151134 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | compressible Navier–Stokes equations, Maxwell–Stefan equations, gaseous mixtures, regular solutions, maximal regularity, decay estimates |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10085757 |
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