CLASSICAL AND NON-CLASSICAL SOLUTIONS OF THE NAVIER-STOKES EQUATION AND ITS SPECIALTY
Keywords:
Navier-Stokes equation, operator, Green's function, Dirichlet boundsAbstract
In the twentieth century, after the first studies of Navier-Stokes and Leray in the 1930s, the attention of mathematicians increased to equations in which the solutions of these equations may be unique and this may be due to turbulence. Leray's work stimulated the significant development of 20th-century functional analysis, and the Navier-Stokes equations are often regarded as one of the two main ancestors of modern 20th-century mathematical analysis, the second being the Schrodinger equation of quantum mechanics.
References
Lectures in Computational Fluid Dynamics of Incompressible Flow: Mathematics, Algorithms and Implementations, James M. McDonough University of Kentucky 2007.
P. J. Roache. Computational Fluid Dynamics. Hermosa Publishers, Albuquerque, NM, 1972.
J. Leray. Etude de diverses équations intégrals non linéaires et de quelques problèmes que pose l'hydrodynamique. J. Math. Pures Appl. 12, 1-82, 1933.
J. Leray. Essai sur les mouvemnts d' un liquide visqueaux que limitent des parois. J. Math. Pures Appl. 13, 331-418, 1934.
O. Ladyzhenskaya. The Mathematical Theory of Viscous Incompressible Flow, revised English edition (translated from the Russian by Richard A. Silverman). Gordon & Breach, New York, 1963.
D. Ruelle and F. Takens. On the nature of turbulence. Comm. Math. Phys. 20, 167- 192, 1971.
E. N. Lorenz. Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130-141, 1963.
S. A. Orszag and G. S. Patterson. Numerical simulation of turbulence: statistical models and turbulence, Lecture Notes in Physics 12, 127-147, Springer-Verlag, Berlin, 1972.
O. Ladyzhenskaya. A dynamical system generated by the Navier-Stokes equations. J. Soviet Math. 3, 458-479, 1973.
O. Ladyzhenskaya. Attractors for Semigroups and Evolution Equations, Cambridge University Press, Cambridge, 1991.
R. Temam. Navier-Stokes Equations: Theory and Numerical Analysis, North- Holland Pub. Co., Amsterdam, 1979. (new edition published by Amer. Math. Soc., Providence, RI, 2001)
R. Temam. Navier-Stokes Equations and Nonlinear Functional Analysis, Soc. Indust. Appl. Math., Philadelphia, 1983. (2 2^"nd " edition published by SIAM, 1995)
R. Temam. Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York, 1988.
P. Constantin and C. Foias. Navier-Stokes Equations, University of Chicago Press, Chicago, 1988.
C. R. Doering and J. D. Gibbon. Applied Analysis of the Navier-Stokes Equations, Cambridge University Press, Cambridge, 1995.
C. Foias, O. Manley, R. Rosa and R. Temam. Navier-Stokes Equations and Turbulence, Cambridge University Press, Cambridge, 2001.
Nasriddinov, O., Abdullayev, J., Jo'rayeva, D., Botirova, N., Maniyozov, O., & Isomiddinova, O. (2024, November). In biology, solving a problem coming to a differential equation in the maple program. In E3S Web of Conferences (Vol. 508, p. 04006). EDP Sciences
Маниёзов, О. А. (2023). Используйте алгоритм фурье для решения линейной задачи для нелинейного уравнения гиперболического типа. Новости образования: исследование в XXI веке, 2(14), 229-233.
Маниёзов, О. (2023, October). Применение преобразования фурье при решении краевой задачи для нелинейного уравнения гиперболического типа. In Conference on Digital Innovation:" Modern Problems and Solutions".
Saidov, M., & Maniyozov, O. (2023, November). Оddiy diffеrеnsial tеnglama uchun bir umumlashgan chеgaraviy masala haqida. In Conference on Digital Innovation:" Modern Problems and Solutions".
Additional Files
Published
How to Cite
License
Copyright (c) 2024 Oybekjon Maniyozov
This work is licensed under a Creative Commons Attribution 4.0 International License.
