

Fundamental problems to equations of compressible chemically reacting flows


Piotr B. Mucha (MIM University of Warsaw) and Milan Pokorny (Faculty
of Mathematics and Physics Charles University in Prague)


Project is carried out by Ewelina Zatorska at University of Warsaw


Models describing the motion of compressible viscous fluids deliver the most challenging
questions in mathematical fluid mechanics. The difficulties relate to the mixed hyperbolicparabolic
type of the system. The analytical theory for the basic NavierStokes equations (including heatconducting
effects) has been recognized in [2, 4]. The aim of this project is to consider models of more complex structure
involving chemical reactions or combustion
The research goal is to prove existence for large data of weak solutions to the full
NavierStokesFourier system coupled with equations describing influence of chemical
reactions in the three dimensional setting. Such models arise from the theory of reacting
gases, cf. [1], and the mathematical results established for one dimensional models. The methods
introduced in [5] should allow to extend the theory on systems with more complex structure. These
mathematical results will be a background for numerical simulations and the chemically reasonable reductions of the system.
[1] J.L. Ericksen, (1998) Introduction to the thermodynamics of solids Appl. Math. Sci., 131, Springer.
[2] E. Feireisl, (2004) Dynamics of Viscous Compressible Fluids Math. Appl., Oxford.
[3] M. Lewicka and P.B. Mucha, (2004) Nonlinear Anal., 57: 951969.
[4] P.L. Lions, (1998) Mathematical topics in fluid mechanics, Vol. 2 Compressible models, Clarendon Press, Oxford Science Publications,
Oxford.
[4] P.L. Lions, (1998) Mathematical topics in fluid mechanics, Oxford Science Publications, Oxford, 2.
[5] P.B. Mucha and M. Pokorny, (2006) t Nonlinearity 19: 17471768.




