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 JAMP  Vol.2 No.4 , March 2014
Global Estimation of the Cauchy Problem Solutions’ the Navier-Stokes Equation
Abstract: The analytic properties of the scattering amplitude are discussed, and a representation of the potential is obtained using the scattering amplitude. A uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided.
Cite this paper: Durmagambetov, A. and Fazilova, L. (2014) Global Estimation of the Cauchy Problem Solutions’ the Navier-Stokes Equation. Journal of Applied Mathematics and Physics, 2, 17-25. doi: 10.4236/jamp.2014.24003.
References

[1]   Russell, J.S. (1844) Report on Waves. Report of the 14th Meeting of the British Association for the Advancement of Science, York, London, 311.

[2]   Russell, J.S. (1838) Report of the Committee on Waves. Report of the 7th Meeting of British Association for the Advancement of Science, John Murray, London, 417-496.

[3]   Ablowitz, M.J. (1981) Harvey Segur Solitons and the Inverse Scattering Transform. Studies in Applied and Numerical Mathematics, Philadelphia, 435. http://dx.doi.org/10.1137/1.9781611970883

[4]   Zabusky, N.J. and Kruskal, M.D. (1965) Interaction of Solitons in a Collisionless Plasma and the Recurrence of Initial States. Physical Review Letters, 15, 240. http://dx.doi.org/10.1103/PhysRevLett.15.240

[5]   Faddeev, L.D. (1974) The Inverse Problem in the Quantum Theory of Scattering. II. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, 3, 93-180.

[6]   Newton, R.G. (1979) New Result on the Inverse Scattering Problem in Three Dimentions. Physical Review Letters, 43, 541-542. http://dx.doi.org/10.1103/PhysRevLett.43.541

[7]   Newton, R.G. (1980) Inverse Scattering Three Dimensions. Journal of Mathematical Physics, 21, 1698-1715.
http://dx.doi.org/10.1063/1.524637

[8]   Somersalo, E., et al. (1988) Inverse Scattering Problem for the Schrodinger’s Equation in Three Dimensions: Connections between Exact and Approximate Methods.

[9]   Povzner, A.Y. (1953) On the Expansion of Arbitrary Functions in Characteristic Functions of the Operator . Matematicheskii Sbornik, 74, 109-156.

[10]   Birman, M. (1961) On the Spectrum of Singular Boundary-Value Problems. Matematicheskii Sbornik, 55, 125-174.

[11]   Poincare, H. (1910) Lecons de Mecanique Celeste.

[12]   Leray, J. (1934) Sur le Mouvement d’un Liquide Visqueux Emplissant l’Espace. Acta Mathematica, 63, 193-248.
http://dx.doi.org/10.1007/BF02547354

[13]   Ladyzhenskaya, O.A. (1970) Mathematic Problems of Viscous Incondensable Liquid Dynamics. Science, 288.

[14]   Solonnikov, V.A. (1964) Estimates Solving Nonstationary Linearized Systems of Navier-Stokes’ Equations. Transactions Academy of Sciences USSR, 70, 213-317.

 
 
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