Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Existence of classical solutions of the equations of motion for compressible fluids of second grade

Author: Š. Matušů-Nečasová
Journal: Quart. Appl. Math. 58 (2000), 369-378
MSC: Primary 76N10; Secondary 35Q35, 76A05
DOI: https://doi.org/10.1090/qam/1753405
MathSciNet review: MR1753405
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Abstract: The existence of the classical solutions has been proved for the equations of motion for compressible fluids of second grade in a bounded domain.

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  • [1] Robert A. Adams, Sobolev spaces, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Pure and Applied Mathematics, Vol. 65. MR 0450957
  • [2] S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II, Comm. Pure Appl. Math. 17 (1964), 35–92. MR 0162050, https://doi.org/10.1002/cpa.3160170104
  • [3] H. Beirão da Veiga, Boundary-value problems for a class of first order partial differential equations in Sobolev spaces and applications to the Euler flow, Rend. Sem. Mat. Univ. Padova 79 (1988), 247–273. MR 964034
  • [4] Lamberto Cattabriga, Su un problema al contorno relativo al sistema di equazioni di Stokes, Rend. Sem. Mat. Univ. Padova 31 (1961), 308–340 (Italian). MR 0138894
  • [5] J. Ernest Dunn and Roger L. Fosdick, Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade, Arch. Rational Mech. Anal. 56 (1974), 191–252. MR 0351249, https://doi.org/10.1007/BF00280970
  • [6] Avner Friedman, Partial differential equations, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1969. MR 0445088
  • [7] Vincenzo Coscia and Giovanni P. Galdi, Existence, uniqueness and stability of regular steady motions of a second-grade fluid, Internat. J. Non-Linear Mech. 29 (1994), no. 4, 493–506. MR 1287760, https://doi.org/10.1016/0020-7462(94)90018-3
  • [8] Giovanni P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations. Vol. I, Springer Tracts in Natural Philosophy, vol. 38, Springer-Verlag, New York, 1994. Linearized steady problems. MR 1284205
    Giovanni P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations. Vol. II, Springer Tracts in Natural Philosophy, vol. 39, Springer-Verlag, New York, 1994. Nonlinear steady problems. MR 1284206
  • [9] J.-L. Lions and E. Magenes, Nonhomogeneous boundary value problems, Vol. I, Springer-Verlag, Berlin, Heidelberg, New York, 1972
  • [10] J. Málek, J. Nečas, and M. Růžička, On the non-Newtonian incompressible fluids, Mathematical Methods and Models in Applied Sciences, Vol. 3, 35-63 (1993)
  • [11] J. Nečas, Theory of multipolar viscous fluids, The mathematics of finite elements and applications, VII (Uxbridge, 1990) Academic Press, London, 1991, pp. 233–244. MR 1132501
  • [12] Antonín Novotný, About steady transport equation. I. 𝐿^{𝑝}-approach in domains with smooth boundaries, Comment. Math. Univ. Carolin. 37 (1996), no. 1, 43–89. MR 1396161
  • [13] M. Padula, Recent contributions and open questions in the mathematical theory of steady motions of viscous compressible fluids, Preprint, 1996
  • [14] K. R. Rajagopal, personal communications
  • [15] R. S. Rivlin and J. L. Ericksen, Stress-deformation relations for isotropic materials, J. Rational Mech. Anal. 4 (1955), 323–425. MR 0068413
  • [16] Roger Temam, On the Euler equations of incompressible perfect fluids, J. Functional Analysis 20 (1975), no. 1, 32–43. MR 0430568
  • [17] J. E. Dunn and K. R. Rajagopal, Fluids of differential type: critical review and thermodynamic analysis, Internat. J. Engrg. Sci. 33 (1995), no. 5, 689–729. MR 1321925, https://doi.org/10.1016/0020-7225(94)00078-X

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DOI: https://doi.org/10.1090/qam/1753405
Article copyright: © Copyright 2000 American Mathematical Society

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