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Dependence of the radial coordinate of a particle on the polar angle in case 2Рис. 3. Dependence of the radial coordinate of a particle on the polar angle in case 329CONCLUSIONS1.2.3.4.5.6.New classes of axially symmetric solutions to the Navier-Stokes equations arefound and studied which can be represented in the form of power series in the radialcoordinate.An axially symmetric solution to the Navier-Stokes equations is found whichexponentially tends to zero for large values of the radial coordinate. It is investigatedin the case of a high Reynolds number when a turbulent flow of a viscous fluid cantake place.An axially symmetric solution to the Navier-Stokes equations is found whichdescribes a case of cavitation that can occur in a viscous fluid.Nonlinear differential equations of the classical Yang-Mills theory are studied.
Inthe case of SU(2) symmetry, new types of their stationary and nonstationaryspherically symmetric solutions are found.New classes of wave solutions to the Yang-Mills solutions are found. Theycontain some types of axially symmetric non-Abelian solutions and non-Abeliansolutions in the form of expanding waves.A study of the dynamic equations for relativistic particles moving in Yukawa’sand Coulomb’s fields. The considered problem is reduced to two nonlinear ordinarydifferential equations of the second and first order. Their numerical investigation iscarried out for different parameters.
It is shown that closed orbits can exist thatcorrespond to some relativistic particles moving in the considered fields.LIST OF THE MAIN WORKS ON THE DISSERTATION TOPICArticles in peer-reviewed journals indexed in the databases Web of Science andScopus1.
Rabinowitch A.S. On a particular solution to the 3D Navier-Stokes equations forliquids with cavitation // Journal of Mathematical Physics, 2016, Vol. 57, No. 8, p.083103-1 – 083103-6.2. Rabinowitch A.S. On a particular analytical solution to the 3D Navier-Stokesequations for high Reynolds numbers // Journal of Mathematical Physics, 2015, Vol.56, No. 9, p. 093101-1 – 093101-8.3.Rabinowitch A.S. On some classes of nonstationary axially symmetric solutions tothe Navier-Stokes equations // Journal of Mathematical Physics Physics, 2014, Vol.55, No. 9, p. 093102-1 – 093102-11.4.
Rabinowitch A.S. Yang-Mills Fields of Nonstationary Spherical Objects with BigCharges // Russian Journal of Mathematical Physics, 2008, Vol. 15, No. 3, p. 389-394.305. Rabinowitch A.S. On a generalization of the Dirac equation for a description of thequark structure of nucleons // Russian Physics Journal, 2008, Vol. 51, No.
8 . p. 822830.6. Rabinowitch A.S. On a new class of non-Abelian expanding waves // Physics LettersB, 2008, Vol. 664, No. 5, p. 295-300.7. Rabinowitch A.S. On non-Abelian expanding waves // Journal of Physics A:Mathematical and Theoretical, 2007, Vol. 40, No. 48, p.
14575–14579.8. Rabinowitch A.S. Exact axially symmetric wave solutions of the Yang-Millsequations // Theoretical and Mathematical Physics, 2006, Vol. 148, No. 2, p. 10811085.9. Rabinowitch A.S. Yang-Mills Equations and Nonlinear Electrodynamics // RussianJournal of Mathematical Physics, 2005, Vol.12, No. 3, p. 379–385.10. Rabinowitch A.S. Generalized Einstein gravitational theory with vacuum vectorialfield // Classical and Quantum Gravity, 2003, Vol.
20, No. 7, p. 1389-1402.11. Rabinowitch A.S. Modified Yang-Mills Theory and Electroweak Interactions //International Journal of Theoretical Physics, 2000, Vol. 39, No. 10, p. 2447-2456.12. Rabinowitch A.S. Nuclear Forces and Neutron Stars // International Journal ofTheoretical Physics, 1998, Vol. 37, No. 5, p. 1477–1489.13. Rabinowitch A.S. Binding Energies of Nuclei // International Journal of TheoreticalPhysics, 1997, Vol. 36, No. 2, p. 533–544.14.
Rabinowitch A.S. Relativistic Theory of Nuclear Forces // International Journal ofTheoretical Physics, 1994, Vol. 33, No. 10, p. 2049–2056.Articles published in Russian peer-reviewed journals15. Rabinowitch A.S. On nonstationary solutions to the Yang-Mills equations // Bulletinof Peoples’ Friendship University of Russia, ser.
Mathematics. Information Sciences.Physics, 2013, № 1, p. 274-283.16. Rabinowitch A.S., Abakumov S.Yu. Nonlinear model of the Earth atmosphere withregard to rocket and satellite data // Bulletin of Peoples’ Friendship University ofRussia, ser. Mathematics. Information Sciences. Physics, 2012, № 3, с.
129-137.17. Рабинович А.С., Абакумов С.Ю. Investigation of a nonlinear model of the Earthupper ionosphere with regard to data derived from spacecrafts // Bulletin of theMoscow State Regional University, ser. Physics and Mathematics, 2012, № 3, с. 5663.18. Rabinowitch A.S., Kramskoy M.A. Periodic orbits of the relativistic antiproton in anonlinear nuclear field А.С. // Bulletin of the Moscow State Regional University, ser.Physics and Mathematics, 2011, № 2, p. 44-52.3119. Rabinowitch A.S.
On a nonlinear generalization of the Yukawa meson theory ofnuclear forces // Bulletin of Peoples’ Friendship University of Russia, ser.Mathematics. Information Sciences. Physics, 2008, № 3, с. 92-98.20. Rabinowitch A.S. Ob odnom obobschenii uravneniya Diraka dlya opisaniyakvarkovoi struktury nuklonov // Izvestiya vuzov.
Fizika, 2008, № 8, с. 44-49.21. Rabinowitch A.S. Tochnye osesimmetrichnye resheniya uravnenii Yanga-Millsa //Teoreticheskaya i matematicheskaya fizika, 2006, т. 148, № 2, с. 243-248.22. Rabinowitch A.S. On nonlinear electrodynamics with Yang-Mills equations //Bulletin of Peoples’ Friendship University of Russia, ser. Physics, 2005, № 13, с. 6877.Other Publications23. Rabinowitch A.S. Mathematical fundamentals of poorly explored anomalous physicalphenomena. – Мoscow: URSS-Librocom, 2015, 328 p.24. Rabinowitch A.S. On axially symmetric solutions of the Navier-Stokes equations //International Journal of Advanced Mathematical Sciences, 2013, Vol.
1, No. 4, p.199-206.25. Rabinowitch A.S. New wave solutions of the Yang-Mills equations with axiallysymmetric sources // International Journal of Advanced Mathematical Sciences, 2013,Vol. 1, No. 3, p. 109-121.26. Rabinowitch A.S. Quantum Yang-Mills Fields in the Superconductive Vacuum //Proceedings of IL All-Russia conference on problems of particle physics, physics ofplasma and condensed media, optoelectronics, Мoscow, Peoples’ FriendshipUniversity of Russia, 2013, p. 15-18.27. Rabinowitch A.S.
On Yang-Mills Equations with Classical Sources // Proceedings ofXLVIII All-Russia conference on problems of particle physics, physics of plasma andcondensed media, optoelectronucs, Мoscow, Peoples’ Friendship University ofRussia, 2012, p. 92-96.28. Rabinowitch A.S., Abakumov S.Yu. Nonlinear Model of the Ionospheric Region FBased on Yang-Mills Theory // Proceedings of XLVIII All-Russia conference onproblems of particle physics, physics of plasma and condensed media, optoelectronics,Мoscow, Peoples’ Friendship University of Russia, 2012, p. 30-33.29. Rabinowitch A.S., Kramskoy M.A. Investigation of closed orbits of nucleons andantinucleons moving in nonlinear nuclear fields // Theoretical Physics: Proceedings ofInternational Conference, Moscow, Moscow State Open University, 2012, p. 232-242.30.
Rabinowitch A.S., Abakumov S.Yu. A new model of the earth atmosphere withstrong electric fields described by means of the Yang-Mills theory // Theoretical32Physics: Proceedings of International Conference, Moscow, Moscow State OpenUniversity, 2012, p. 94-103.31. Rabinowitch A.S., Abakumov S.Yu. А.С. Nonlinear model of the Earth ionosphere //New Information Technology. Proceedings of XV All-Russia Scientific andEngineering Conference, Moscow, Moscow State University of InstrumentEngineering and Informatics, 2012, p. 49-54.32.
Rabinowitch A.S. On New Solutions of Classical Yang-Mills Equations withCylindrical Sources // Applied Mathematics, 2010, Vol. 1, No. 1, p. 1-7.33. Rabinowitch A.S., Kramskoy M.A. Investigation of periodic orbits of nucleons andantinucleons in a nonlinear field of nuclear forces // Bulletin of Moscow StateUniversity of Instrument Engineering and Informatics, 2010, № 29, p. 112-122.34. Rabinowitch A.S. Nonlinear Physical Fields and Anomalous Phenomena.- NewYork: Nova Science Publishers, Inc., 2009, 245 p.35.
Rabinowitch A.S. On a nonlinear theory of strong electromagnetic fields // RecentProblems in Field Theory, Kazan, Kazan State University, 2005, Vol. 5, p. 205-212..
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