Existence of a Solution “in the Large” for Ocean Dynamics Equations
Existence of a Solution “in the Large” for Ocean Dynamics Equations
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DOI：
10.1007/s00021-006-0228-4
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发表时间：
2007-07
影响因子：
1.3
通讯作者：
G. M. Kobel’kov
中科院分区：
文献类型：
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作者：
G. M. Kobel’kov
对于描述大尺度海洋动力学的方程组，“大范围”证明了存在唯一性定理。该系统是通过在 z 方向域较小的假设下改变垂直速度分量 u3 的方程，并添加密度函数 ρ 的非线性方程，从 3D 纳维-斯托克斯方程获得的。更准确地说，证明了对于任意时间间隔 [0,T]，任意粘度系数和任意初始条件 $${\hat{\bfu u}}_{0} = (u_1, u_2) \in W_{2}^{2}(\Omega), \quad \int_{0}^{1}(\partial_{1}u_{1} + \partial_{2}u_{2})dz = 0， \quad \rho_{0} \in W_{2}^{2}(\Omega),$$存在弱解且唯一，且范数是连续整数。
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 componentu3under the assumption of smallness of a domain inz-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 andand the normsare continuous int.