{"title":"On the Strong Solutions of the Nonlinear Viscous Rotating Stratified Fluid","authors":"A. Giniatoulline","volume":118,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":475,"pagesEnd":482,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10005420","abstract":"A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.","references":"[1]\tB. Cushman-Roisin, and J. Beckers, Introduction to Geophysical Fluid Dynamics, New York: Acad. Press, 2011, ch3.\r\n[2]\tD. Tritton, Physical Fluid Dynamics, Oxford: Oxford UP, 1990, ch.2.\r\n[3]\tA. Aloyan, \u201cNumerical modeling of remote transport of admixtures in atmosphere,\u201d Numerical Methods in the Problems of Atmospheric Physics and Environment Protection, Novosibirsk: Ac. Sci. USSR, 1985, pp. 55-72.\r\n[4]\tR. Temam, Navier-Stokes Equations: Theory and Numerical Analysis, New York: AMS Chelsea Publishing, 2000.\r\n[5]\tL. Tartar, An Introduction to Navier-Stokes Equations and Oceanography, Berlin: Springer, 2006.\r\n[6]\tH. Sohr, The Navier-Stokes Equations: An Elementary Functional Analytic Approach, Zurich: Birkh\u00e4user, 2012.\r\n[7]\tA. Giniatoulline, and T. Castro, \u201cOn the Spectrum of Operators of Inner Waves in a Viscous Compressible Stratified Fluid,\u201d Journal Math. Sci. Univ. of Tokyo, 2012, no. 19, pp. 313-323.\r\n[8]\tA. Giniatoulline, and T. Castro, \u201cOn the Existence and Uniqueness of Solutions for Nonlinear System Modeling Three-Dimensional Viscous Stratified Flows,\u201d Journal of Applied Mathematics and Physics, 2014, no. 2, pp. 528-539.\r\n[9]\tO. Ladyzhenskaya, The Mathematical Theory of the Viscous Incompressible Flow, New York: Gordon and Breach, 1969.\r\n[10]\tL. Cattabriga, \u201cSu un Problema al Contorno Relativo al Sistema di Equazioni di Stokes,\u201d Rendiconti del Seminario Matematico della Universita di Padova, 1961, vol. 31, pp. 308-340.\r\n[11]\tV. Maslennikova, and M. Bogovski, \u201cElliptic Boundary Value Problems in Unbounded Domains with Noncompact and Nonsmooth Boundaries,\u201d Milan Journal of Mathematics, 1986, no. 56, vol. 1, pp.125-138.\r\n[12]\tT. Kato, Perturbation theory for Linear Operators, Berlin: Springer, 1966.\r\n[13]\tS. Agmon, A. Douglis, and L. Nirenberg, \u201cEstimates Near the Boundary for Solutions of Elliptic Differential,\u201d Comm. Pure and Appl. Mathematics, 1964, vol. 17, pp. 35-92.\r\n[14]\tA. Giniatoulline, \u201cMathematical Study of Some Models of the Atmosphere Dynamics Counting with Heat Transfer and Humidity,\u201d Recent Advances on Computational Science and Applications, Seoul: WSEAS Press, 2015, vol. 52, pp. 55-61.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 118, 2016"}