research partners    
Ph.D. students    
consortium members    

Piotr Gwiazda
Institute of Applied Mathematics and Mechanics
University of Warsaw
Banacha 2,
02-097 Warsaw
phone: +48 22 5544551
fax: +48 22 5544700

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 hyperbolic-parabolic type of the system. The analytical theory for the basic Navier-Stokes equations (including heat-conducting 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 Navier-Stokes-Fourier 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: 951--969.
[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: 1747-1768.