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Global 1 Estimation of the Cauchy Problem Solutions to the Navier-Stokes Equation

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DOI: 10.4236/am.2014.513184    2,226 Downloads   2,757 Views  

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. The paper also describes the time blowup of classical solutions for the Navier-Stokes equations by the smoothness assumption.

 

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Durmagambetov, A. and Fazilova, L. (2014) Global 1 Estimation of the Cauchy Problem Solutions to the Navier-Stokes Equation. Applied Mathematics, 5, 1903-1912. doi: 10.4236/am.2014.513184.

References

[1] Durmagambetov, A.A. and Fazilova, L.S. (2014) Global Estimation of the Cauchy Problem Solutions’ the Navier-Stokes Equation. Journal of Applied Mathematics and Physics, 2, 17-25.
http://dx.doi.org/10.4236/jamp.2014.24003
[2] Russell, J.S. (1844) Report on Wave. Report of the 14th Meeting of the British Association for the Advancement of Science, York, September 1844 (London 1845), Plates XLVII-LVII, 90-311.
[3] 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.
[4] Ablowitz, M.J. and Segur, H. (1981) Solitons and the Inverse Scattering Transform SIAM, 435-436.
[5] 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, 240-243.
http://dx.doi.org/10.1103/PhysRevLett.15.240
[6] Faddeev, L.D. (1974) The Inverse Problem in the Quantum Theory of Scattering. II. Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., VINITI, Moscow, 93, 180.
[7] Newton, R.G. (1979) New Result on the Inverse Scattering Problem in Three Dimensions. Physical Review Letters, 43, 541-542.
http://dx.doi.org/10.1103/PhysRevLett.43.541
[8] Newton, R.G. (1980) Inverse Scattering in Three Dimensions. Journal of Mathematical Physics, 21, 1698-1715.
http://dx.doi.org/10.1063/1.524637
[9] Somersalo, E., et al. (1988) Inverse Scattering Problem for the Schrodinger’s Equation in Three Dimensions: Connections between Exact and Approximate Methods.
http://conservancy.umn.edu/bitstream/4896/1/449.pdf
[10] Povzner, A.Y. (1953) On the Expansion of Arbitrary Functions in Characteristic Functions of the Operator . Russian Matematicheskii Sbornik, 32, 109.
[11] Birman, M.S. (1961) On the Spectrum of Singular Boundary-Value Problems. Russian Matematicheskii Sbornik, 55, 125.
[12] Poincare, H. (1910) Lecons de mecanique celeste. t. 3, 347-349.
[13] 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
[14] Ladyzhenskaya, O.A. (1970) Mathematics Problems of Viscous Incondensable Liquid Dynamics. M:Science, 288.
[15] Solonnikov, V.A. (1964) Estimates Solving Nonstationary Linearized Systems of Navier-Stokes’ Equations. Transactions Academy of Sciences USSR, 70, 213-317.
[16] Huang, X.D. and Li, J. and Wang, Y. (2013) Serrin-Type Blowup Criterion forFull Compressible Navier-Stokes System. Archive for Rational Mechanics and Analysis, 207, 303-316.
http://dx.doi.org/10.1007/s00205-012-0577-5
[17] Terence Tao (2014) Finite Time Blowup for an Averaged Three-Dimensional Navier-Stokes Equation. arXiv:1402. 0290 [math. AP]

  
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