Glasnik Matematicki, Vol. 46, No.1 (2011), 215-231.

THE CAUCHY PROBLEM FOR ONE-DIMENSIONAL FLOW OF A COMPRESSIBLE VISCOUS FLUID: STABILIZATION OF THE SOLUTION

Nermina Mujaković and Ivan Dražić

Department of Mathematics, University of Rijeka, Omladinska 14, 51 000 Rijeka, Croatia
e-mail: mujakovic@inet.hr

Faculty of Engineering, University of Rijeka, Vukovarska 58, 51 000 Rijeka, Croatia
e-mail: idrazic@riteh.hr


Abstract.   We analyze the Cauchy problem for non-stationary 1-D flow of a compressible viscous and heat-conducting fluid, assuming that it is in the thermodynamical sense perfect and polytropic. This problem has a unique generalized solution on R × ]0,T[ for each T>0. Supposing that the initial functions are small perturbations of the constants and using some a priori estimates for the solution independent of T, we prove a stabilization of the solution.

2000 Mathematics Subject Classification.   46E35, 35B40, 35B45, 76N10.

Key words and phrases.   Compressible viscous fluid, the Cauchy problem, stabilization.


Full text (PDF) (access from subscribing institutions only)

DOI: 10.3336/gm.46.1.16


References:

  1. S. N. Antontsev, A. V. Kazhykhov and V. N. Monakhov, Boundary value problems in mechanics of nonhomogeneous fluids, North-Holland, Amsterdam, 1990.
    MathSciNet    

  2. R. Dautray and J. L. Lions, Mathematical analysis and numerical methods for science and techonology. Vol. 2, Springer-Verlag, Berlin, 1988.
    MathSciNet    

  3. R. Dautray and J. L. Lions, Mathematical analysis and numerical methods for science and techonology. Vol. 5, Springer-Verlag, Berlin, 1992.
    MathSciNet    

  4. Ya. I. Kanel', Cauchy problem for equations of gas dynamics with viscosity, Sibirsk. Mat. Zh. 20 (1979), 293-306.
    MathSciNet    

  5. N. Mujaković, One-dimensional flow of a compressible viscous micropolar fluid: The Cauchy problem, Math. Commun. 10 (2005), 1-14.
    MathSciNet    

  6. N. Mujaković, Uniqueness of a solution of the Cauchy problem for one-dimensional compressible viscous micropolar fluid model, Appl. Math. E-Notes 6 (2006), 113-118.
    MathSciNet    

Glasnik Matematicki Home Page