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References
M. Arnold. In Preparation
A. Bressan ≪Current Research Directions in Hyperbolic Systems of Conservation Laws ≫Notiziario della Unione Matematica Italiana, Decembre 2004, Supplemento al N12
M. Cannone, F. Planchon. ≪On the reqularity of the bilinear term of solutions of the incompressible Navier–Stokes equationsin ℝ 3.≫Rev. Mathematica Americana, vol. 1, 2000, 1–16
Weinan E, Ya. Sinai ≪Recent Results on Mathematical and Statistical Hydrodynamics.≫Russian Math. Surveys, 55, N4, 635–666, 2000
Weinan E, K. Khanin, A. Mazel, Ya. Sinai ≪Invariant measure for Burgers Equation with random forcing≫Ann. of Math. 151, 2000, 877–960
Weinan E, K. Khanin, A. Mazel, Ya. Sinai ≪Probability distribution function for the random forced Burgers Equation.≫Phys. Rev. Lett. 78, 1997, 1904–1907
C. Foias and R. Temam ≪Gevrey classes of regularity for the solutions of the Navier–Stokes equations.≫J. of Func. Anal 87, 1989, 359–369
T. Kato ≪Strong L p Solutions of the Navier–Stokes Equation in ℝ m, with applications to weak solutions.≫Mathematische Zeitschrift, 187, 1984, 471–480
P. Lax ≪Hyperbolic Systems of Conservation Laws, II.≫Comm. Pure and Appl. Math. 10, 1957, 537–556
Y. Le Jan and A.S. Sznitman ≪Stochastic Cascades and 3–dimensional Navier–Stokes Equations.≫Probability Theory and Related Fields, 109, 1997, 343–366
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, 497–516
O.Oleinik≪Discontinous Solutionsofnon-lineardifferential equations.≫ Uspekhi Math. Nauk, 12, 1957, 2–73
Ya.G. Sinai ≪On the Local and Global Existence and Uniqueness of Solutions of the 3D–Navier–Stokes System on ℝ 3.≫Perspectives in Analysis. Conference in honor of L. Carleson 75-th birthday. Springer-Verlag, to appear
Ya.G. Sinai ≪Power Series for Solutions of the Navier–Stokes System on ℝ 3.≫Journal of Stat. Physics, 121, 2005, 779–803
Ya.G. Sinai ≪Diagrammatic Approach to the 3D–Navier–Stokes System.≫Russian Math. Journal, vol. 60, N5, 2005, 47–70
Ya.G. Sinai ≪Two results concerning asymptotic behavior of solutions of the Burgers equation with force.≫Journal of Stat. Physics, 64, 1992, 1–12
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Sinai, Y.G. (2008). Mathematical Results Related to the Navier–Stokes System. In: Da Prato, G., Rückner, M. (eds) SPDE in Hydrodynamic: Recent Progress and Prospects. Lecture Notes in Mathematics, vol 1942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78493-7_3
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