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Original Articles

An L2-maximal regularity result for the evolutionary Stokes–Fourier system

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Pages 31-45 | Received 03 Feb 2010, Accepted 21 Feb 2010, Published online: 19 Aug 2010

References

  • Ladyzhenskaya , OA . 1969 . “ The Mathematical Theory of Viscous Incompressible Flow ” . In 2nd English Edition, Revised and Enlarged. (Translated from the Russian Richard A. Silverman and John Chu. Mathematics and its Applications , Vol. 2 , New York : Gordon and Breach Science Publishers .
  • Solonnikov , VA . 1964 . Estimates for solutions of a non-stationary linearized system of Navier–Stokes equations . Trudy Mat. Inst. Steklov. , 70 : 213 – 317 .
  • Bulíček , M , Feireisl , E and Málek , J . 2009 . A Navier–Stokes–Fourier system for incompressible fluids with temperature dependent material coefficients . Nonlinear Anal. Real World Appl. , 10 : 992 – 1015 .
  • Bulíček , M , Málek , J and Rajagopal , K . 2009 . Mathematical analysis of unsteady flows of fluids with pressure, shear-rate, and temperature dependent material moduli that slip at solid boundaries . SIAM J. Math. Anal. , 41 : 665 – 707 .
  • E. Feireisl and J. Málek, On the Navier–Stokes equations with temperature-dependent transport coefficients, Differ. Eqns Nonlinear Mech. (2006), Art. ID 90616, pp. 1–14.
  • V.A. Solonnikov, L p -estimates for solutions to the initial boundary-value problem for the generalized Stokes system in a bounded domain, J. Math. Sci. (New York) 105 (2001), pp. 2448–2484 (Function Theory and Partial Differential Equations).
  • Ladyženskaja , OA , Solonnikov , VA and Ural′ceva , NN . 1967 . “ Linear and Quasilinear Equations of Parabolic Type ” . In (Translated from the Russian by S. Smith. Translations of Mathematical Monographs , Vol. 23 , Providence, RI : American Mathematical Society .

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