Abstract
In this work, we prove the local well-posedness of strong solutions to the compressible flow of a chemically reacting gaseous mixture with the initial data containing vacuum. Moreover, we should emphasize that there is no assuming compatibility condition on the initial data.
Similar content being viewed by others
References
Chen, G.-Q., Hoff, D., Trivisa, K.: On the Navier–Stokes equations for exothermically reacting compressible fluids. Acta Math. Appl. Sin. 18, 15–36 (2002)
Chen, G.-Q., Hoff, D., Trivisa, K.: Global solutions to a model for exothermically reacting, compressible flows with large discontinuous initial data. Arch. Ration. Mech. Anal. 166, 321–358 (2003)
Chen, G.-Q., Hoff, D., Trivisa, K.: Analysis on models for exothermically reacting, compressible flows with large discontinuous initial data. Contemp. Math. 371, 73–91 (2005)
Donatelli, D., Trivisa, K.: A multidimensional model for the combustion of compressible fluids. Arch. Ration. Mech. Anal. 185, 379–408 (2007)
Donatelli, D., Trivisa, K.: On the motion of a viscous compressible radiative-reacting gas. Commun. Math. Phys. 265, 463–491 (2006)
Donatelli, D., Trivisa, K.: From the dynamics of gaseous stars to the incompressible Euler equations. J. Differ. Equ. 245, 1356–1385 (2008)
Donatelli, D., Feireisl, E., Novotný, A.: Scale analysis of a hydrodynamic model of plasma. Math. Models Methods Appl. Sci. 25, 371–394 (2015)
Ducomet, B.: Hydrodynamical models of gaseous stars. Rev. Math. Phys. 8, 957–1000 (1996)
Feireisl, E., Novotný, A.: On a simple model of reacting flows arising in astrophysics. Proc. R. Soc. Edinb. 135, 1169–1194 (2005)
Feireisl, E., Petzeltová, H., Trivisa, K.: Multicomponent reactive flows: global-in-time existence for large data. Commun. Pure Appl. Anal. 7, 1017–1047 (2008)
Giovangigli, V.: Mulitcomponent Flow Modeling. Birkhäuser, Basel (1957)
Gong, H., Li, J., Liu, X., Zhang, X.: Local well-posedness of isentropic compressible Navier–Stokes equations with vacuum. Commun. Math. Sci. 18, 1891–1909 (2020)
Huang, X.: On local strong and classical solutions to the three-dimensional barotropic compressible Navier–Stokes equations with vacuum. Sci. China Math. (2019). https://doi.org/10.1007/s11425-019-9755-3
Kwon, Y.-S.: Convergence of the flow of a chemically reacting gaseous mixture to incompressible Euler equations in a unbounded domain. Z. Angew. Math. Phys. 68, Paper No. 131, 16 pp (2017)
Mucha, P.B., Pokorný, M., Zatorska, E.: Heat-conducting, compressible mixtures with multicomponent diffusion: construction of a weak solution. SIAM J. Math. Anal. 47, 3747–3797 (2015)
Mucha, P.B., Pokorný, M., Zatorska, E.: Chemically reacting mixtures in terms of degenerated parabolic setting. J. Math. Phys. 54, 071501 (2013)
Mucha, P.B., Pokorný, M., Zatorska, E.: Approximate solutions to a model of two-component reactive flow. Discrete Contin. Dyn. Syst. Ser. S 7, 1079–1099 (2014)
Piasecki, T., Pokorný, M.: Weak and variational entropy solutions to the system describing steady flow of a compressible reactive mixture. Nonlinear Anal. 159, 365–392 (2017)
Vol’pert, A.I., Hudjaev, S.I.: The Cauchy problem for composite systems of nonlinear differential equations. Math. USSR SB. 16, 504–528 (1972)
Acknowledgements
We are very much indebted to the anonymous referees for many helpful suggestions. The research of Tong Tang is supported by the NSFC Grant No. 11801138.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Tang, T., Sun, J. Local well-posedness for the flow of a chemically reacting gaseous mixture. Z. Angew. Math. Phys. 72, 197 (2021). https://doi.org/10.1007/s00033-021-01623-6
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00033-021-01623-6