caa a22 4500 463171039 CHVBK 20180406164813.0 cr unu---uuuuu 170326e20071201xx s 000 0 eng 10.1007/s00021-006-0228-4 doi (NATIONALLICENCE)springer-10.1007/s00021-006-0228-4 Kobelkov Georgy Department of Mechanics and Mathematics, Moscow State University, 119899, Moscow, Russia aut Existence of a Solution "in the Large” for Ocean Dynamics Equations [Elektronische Daten] [Georgy Kobelkov] Abstract.: For the system of equations describing the large-scale ocean dynamics, an existence and uniqueness theorem is proved "in the large”. This system is obtained from the 3D Navier-Stokes equations by changing the equation for the vertical velocity component u 3 under the assumption of smallness of a domain in z-direction, and a nonlinear equation for the density function ρ is added. More precisely, it is proved that for an arbitrary time interval [0, T], any viscosity coefficients and any initial conditions $${\hat{\bf u}}_{0} = (u_1, u_2) \in W_{2}^{2}(\Omega), \quad \int_{0}^{1}(\partial_{1}u_{1} + \partial_{2}u_{2})dz = 0, \quad \rho_{0} \in W_{2}^{2}(\Omega),$$ a weak solution exists and is unique and $${\hat{\bf u}}_{x_3} \in {\bf W}_{2}^{1}(Q_T), \rho_{x_{3}} \in W_{2}^{1}(Q_T)$$ and the norms $$\|\nabla{\hat{\bf u}}\|_{\Omega}, \|\nabla \rho \|_{\Omega}$$ are continuous in t. Birkhaueser, 2007 Ocean dynamics equations nationallicence primitive equations nationallicence nonlinear partial differential equations nationallicence Journal of Mathematical Fluid Mechanics SP Birkhäuser Verlag Basel 9/4(2007-12-01), 588-610 1422-6928 9:4<588 2007 9 21 https://doi.org/10.1007/s00021-006-0228-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00021-006-0228-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kobelkov Georgy Department of Mechanics and Mathematics, Moscow State University, 119899, Moscow, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Fluid Mechanics SP Birkhäuser Verlag Basel 9/4(2007-12-01), 588-610 1422-6928 9:4<588 2007 9 21 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer