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Existence, uniqueness and Lq-estimates for the stokes problem in an exterior domain

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References

  • Agmon, S., Douglis, A. &Nirenberg, L., 1964,Estimates near the boundary of solutions of elliptic partial differential equations satisfying general boundary conditions, II, Comm. Pure Appl. Math.,17, 35–92.

    Article  MATH  MathSciNet  Google Scholar 

  • Bogovskii, M. E., 1979,Solution if the first boundary value problem for the equation on continuity of an incompressible medium, Sov. Mat. Dokl.,20, 1094–1098.

    Google Scholar 

  • Borchers, W. & Miyakawa, T., 1989,Algebraic L 2 decay for the Navier Stokes flows if exterior domains, Preprint, Universität Paderborn.

  • Cattabriga, L., 1961,Su un problema al contorno relativo al sistema di equazioni di Stokes, Rend. Sem. Mat. Padova31, 308–340.

    MATH  MathSciNet  Google Scholar 

  • Chang, I. D., &Finn, R., 1961,On the solutions of a class of equations occurring in continuum mechanics with application to the Stokes paradox, Arch. Rational Mech. Anal.7, 388–401.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Gagliardo, E., 1957,Caratterizzazioni delle tracce sulla frontiera relative and alcune classi di funzioni in n variabili, Rend. Sem. Mat. Padova27, 284–305.

    MATH  MathSciNet  Google Scholar 

  • Galdi, G. P., (forthcoming),An introduction to the mathematical theory of the Navier-Stokes equations, Springer Tracts in Natural Philosophy.

  • Galdi, G. P. &Maremonti, P., 1986,Monotonic decreasing and asymptotic behavior of the kinetic energy for weak solutions of the Navier-Stokes equations in exterior domains, Arch. Rational Mech. Anal.94, 253–266.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Giga, Y., 1981,Analyticity of the semigroup generated by the Stokes operator in L r spaces, Math. Z.178, 297–329.

    Article  MATH  MathSciNet  Google Scholar 

  • Giga, Y., 1985.Domains of fractional powers of the Stokes operator in L r spaces, Arch. Rational Mech. Anal.89, 251–265.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Kozono, H. & Sohr, H., 1989,L q-regularity theory of the Stokes equations in exterior domains, Preprint, Universität Paderborn.

  • Ladyzhenskaya, O. A., 1959,Investigation of the Navier-Stokes equation for a stationary flow of an incompressible fluid, Usp. Mat. Nauk (3)14, 75–97.

    MATH  Google Scholar 

  • Ladyzhenskaya, O. A., 1969,The mathematical theory of viscous incompressible flow, Gordon & Breach.

  • Lax, P. D., 1955,On Cauchy's problem for hyperbolic equations and the differentiability of solutions of elliptic equations, Comm. Pure Appl. Math.8, 615–633.

    Article  MATH  MathSciNet  Google Scholar 

  • Maremonti, P. &Solonnikov, V. A., 1985,Estimates for the Laplace operator in exterior domains, (in Russian) Zap. Nauk. Sem. LOMI146, 92–102.

    MATH  MathSciNet  Google Scholar 

  • Maremonti, P. & Solonnikov, V. A., 1986,Su una disequaglianza per le soluzioni del problema di Stokes in domini esterni, Preprint, Universìtà di Napoli.

  • Maslennikova, V. N. &Bogovskii, M. E., 1978,Denseness of finite solenoidal vector fields (in Russian), Sib. Mat. Zh.19, 1092–1108.

    MATH  MathSciNet  Google Scholar 

  • Miranda, C., 1978,Istituzioni di analisi funzionale lineare, U.M.I., Oderisi da Gubbio Editrice.

  • Nečas, J., 1967,Les méthodes directes en théorie des équations elliptiques, Masson et Cie.

  • Simader, C. G., 1972,On Dirichlet's boundary value problem, Lecture Notes in Mathematics, Vol. 268, Springer-Verlag.

  • Simader, C. G. & Sohr, H., (forthcoming),A new approach to the Helmholtz decomposition in L q-spaces for bounded and exterior domains.

  • Smirnov, V. I., 1964,A course of higher mathematics, Vol. V, Pergamon Press.

  • Sobolev, S. L., 1963,Denseness of finite fields in the space L mp (En) (in Russian), Sib. Mat. Zh.3, 673–682.

    MathSciNet  Google Scholar 

  • Sobolevskii, P. E., 1960,On the smoothness of generalized solutions of the Navier-Stokes equations, Soviet Mat. Dokl.131, 341–343.

    MathSciNet  Google Scholar 

  • Solonnikov, V. A., 1960,On the estimates of the tensor Green function for some boundary-value problems, Soviet Mat. Dokl.130, 988–991.

    MathSciNet  Google Scholar 

  • Solonnikov, V. A., 1966,On general boundary-value problems for elliptic systems in the sense of Douglis-Nirenberg, II, Trudy Mat. Inst. Steklov92, 233–297.

    MathSciNet  Google Scholar 

  • Solonnikov, V. A., 1977,Estimates of solutions of nonstationary Navier-Stokes equations, J. Sov. Math.8, 467–529.

    Article  MATH  Google Scholar 

  • Solonnikov, V. A. &Sčadilov, V. E., 1973,On a boundary value problem for a stationary system of Navier-Stokes equations, Trudy Mat. Inst. Steklov125, 196–199.

    MathSciNet  Google Scholar 

  • Stokes, G., 1856, seeMathematical and physical papers, Cambridge Univ. Press.

  • Temam, R., 1977,Navier-Stokes equations, North Holland.

  • Vorovich, I. I. &Youdovich, V. I., 1961,Stationary flow of a viscous incompressible fluid (in Russian), Mat. Sborn.53, 391–428.

    Google Scholar 

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Communicated by J. Serrin

A Lamberto Cattabriga, in Memoria

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Galdi, G.P., Simader, C.G. Existence, uniqueness and Lq-estimates for the stokes problem in an exterior domain. Arch. Rational Mech. Anal. 112, 291–318 (1990). https://doi.org/10.1007/BF02384076

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