Spectral analysis of linearized stationary equations of a compressible viscous fluid
Sbornik. Mathematics, Tome 198 (2007) no. 10, pp. 1495-1515 Cet article a éte moissonné depuis la source Math-Net.Ru

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The spectrum of an operator on a torus described by linearized stationary equations of a compressible viscous fluid is considered. These equations are obtained by the linearization of non-linear equations of a compressible viscous fluid at an arbitrary solution depending on the $x$-variable. It is shown that the spectrum of the operator is a discrete point set, which lies in a sector of the complex plane that is symmetric relative to the real axis and has its vertex on the positive half-axis. Bibliography: 10 titles.
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M. A. Pribyl. Spectral analysis of linearized stationary equations of a compressible viscous fluid. Sbornik. Mathematics, Tome 198 (2007) no. 10, pp. 1495-1515. http://geodesic.mathdoc.fr/item/SM_2007_198_10_a5/

[1] Y. Kagei, T. Kobayashi, “Asymptotic behavior of solutions of the compressible Navier–Stokes equations on the half space”, Arch. Ration. Mech. Anal., 177:2 (2005), 231–330 | DOI | MR | Zbl

[2] A. Matsumura, T. Nishida, “The initial value problem for the equations of motion of compressible viscous and heat-conductive fluids”, Proc. Japan Acad. Ser. A Math. Sci., 55:9 (1979), 337–342 | DOI | MR | Zbl

[3] A. Matsumura, T. Nishida, “The initial value problem for the equations of motion of viscous and heat-conductive gases”, J. Math. Kyoto Univ., 20:1 (1980), 67–104 | MR | Zbl

[4] M. Núñez, “Spectral analysis of viscous static compressible fluid equilibria”, J. Phys. A, 34:20 (2001), 4341–4352 | DOI | MR | Zbl

[5] A. V. Fursikov, “Stabilizability of a quasi-linear parabolic equation by means of a boundary control with feedback”, Sb. Math., 192:4 (2001), 593–639 | DOI | MR | Zbl

[6] A. V. Fursikov, “Stabilizatsiya s granitsy reshenii sistemy Nave–Stoksa: razreshimost i obosnovanie chislennogo modelirovaniya”, Dalnevost. matem. zhurn., 4:1 (2003), 86–100 | MR

[7] M. A. Pribyl, “Spektralnyi analiz linearizovannykh statsionarnykh uravnenii vyazkoi szhimaemoi zhidkosti, zadannykh v $\mathbb R^3$ s periodicheskimi kraevymi usloviyami”, Algebra i analiz, 20:2 (2008), 149–177 | MR

[8] D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Math., 840, Springer-Verlag, Berlin–New York, 1981 | DOI | MR | MR | Zbl | Zbl

[9] L. Hörmander, The analysis of linear partial differential operators. Vol. III: Pseudodifferential operators, Grundlehren Math. Wiss., 274, Springer-Verlag, Berlin, 1985 | MR | MR | Zbl

[10] I. C. Gohberg, M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators, Transl. Math. Monogr., 18, Amer. Math. Soc., Providence, RI, 1969 | MR | MR | Zbl