Advertisement

Mathematical Results Related to the Navier–Stokes System

  • Yakov G. Sinai
Part of the Lecture Notes in Mathematics book series (LNM, volume 1942)

Keywords

Partition Function Main Shock Hyperbolic System Burger Equation Mathematical Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A1.
    M. Arnold. In PreparationGoogle Scholar
  2. B1.
    A. Bressan ≪Current Research Directions in Hyperbolic Systems of Conservation Laws ≫Notiziario della Unione Matematica Italiana, Decembre 2004, Supplemento al N12Google Scholar
  3. CP.
    M. Cannone, F. Planchon. ≪On the reqularity of the bilinear term of solutions of the incompressible Navier–Stokes equationsin 3.≫Rev. Mathematica Americana, vol. 1, 2000, 1–16MathSciNetGoogle Scholar
  4. ES.
    Weinan E, Ya. Sinai ≪Recent Results on Mathematical and Statistical Hydrodynamics.≫Russian Math. Surveys, 55, N4, 635–666, 2000MATHCrossRefMathSciNetGoogle Scholar
  5. EKMS1.
    Weinan E, K. Khanin, A. Mazel, Ya. Sinai ≪Invariant measure for Burgers Equation with random forcing≫Ann. of Math. 151, 2000, 877–960MATHCrossRefMathSciNetGoogle Scholar
  6. EKMS2.
    Weinan E, K. Khanin, A. Mazel, Ya. Sinai ≪Probability distribution function for the random forced Burgers Equation.≫Phys. Rev. Lett. 78, 1997, 1904–1907CrossRefGoogle Scholar
  7. FT.
    C. Foias and R. Temam ≪Gevrey classes of regularity for the solutions of the Navier–Stokes equations.≫J. of Func. Anal 87, 1989, 359–369MATHCrossRefMathSciNetGoogle Scholar
  8. K1.
    T. Kato ≪Strong L p Solutions of the Navier–Stokes Equation in m, with applications to weak solutions.≫Mathematische Zeitschrift, 187, 1984, 471–480Google Scholar
  9. L.
    P. Lax ≪Hyperbolic Systems of Conservation Laws, II.≫Comm. Pure and Appl. Math. 10, 1957, 537–556MATHCrossRefMathSciNetGoogle Scholar
  10. LJS.
    Y. Le Jan and A.S. Sznitman ≪Stochastic Cascades and 3–dimensional Navier–Stokes Equations.≫Probability Theory and Related Fields, 109, 1997, 343–366MATHCrossRefMathSciNetGoogle Scholar
  11. MS.
    J. Mattingly, Ya. G. Sinai ≪An Elementary Proof of the Existence and Uniqueness Theorem for the Navier–Stokes Equations.≫Comm. in Contemporery Mathematics, vol. 1, N4, 1999, 497–516MATHCrossRefMathSciNetGoogle Scholar
  12. O.
    O.Oleinik≪Discontinous Solutionsofnon-lineardifferential equations.≫ Uspekhi Math. Nauk, 12, 1957, 2–73Google Scholar
  13. S1.
    Ya.G. Sinai ≪On the Local and Global Existence and Uniqueness of Solutions of the 3D–Navier–Stokes System on 3.≫Perspectives in Analysis. Conference in honor of L. Carleson 75-th birthday. Springer-Verlag, to appearGoogle Scholar
  14. S2.
    Ya.G. Sinai ≪Power Series for Solutions of the Navier–Stokes System on 3.≫Journal of Stat. Physics, 121, 2005, 779–803MATHCrossRefMathSciNetGoogle Scholar
  15. S3.
    Ya.G. Sinai ≪Diagrammatic Approach to the 3D–Navier–Stokes System.≫Russian Math. Journal, vol. 60, N5, 2005, 47–70MathSciNetGoogle Scholar
  16. S4.
    Ya.G. Sinai ≪Two results concerning asymptotic behavior of solutions of the Burgers equation with force.≫Journal of Stat. Physics, 64, 1992, 1–12CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Yakov G. Sinai
    • 1
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

Personalised recommendations