Well posedness of the initial value problem for vertically discretized hydrostatic equations

摘要

Vertically discretized linearized hydrostatic equations in hybrid coordinates are considered. The matrix of vertical structure, which depends on vertical discretization and determines the classification of the obtained system of time-dependent partial differential equations, is derived. The main theorem about oscillatory properties of the matrix of vertical structure is proved. This result ensures the well posedness of the initial value problem for vertically discretized primitive equations. [References: 39]