5月7日：范恩贵

：范恩贵 教授

：陈勇教授

In this paper, we construct two kinds of interesting explicit analytical solutions for n-dimensional Boussinesq equations without viscosity. The first kind is Cartesian linear analytical solutions with respect to velocity field u=(u_1, u_n), The first n-1 velocity field (u_1,, u_{n-1}) can be can be characterized by  a linear transformation of a matrix A with respect to coordinates of spital variables; while last velocity u_n is characterized by the trace of the matrix A; The pressure p and temperature \theta are related to the well-known heat equation. The technique used here is matrix and curve integration theory to transform analytically solving the n-dimensional Boussinesq equations into algebraically constructing an appropriate matrix. The second kind is nonlinear solutions with respect to velocity field u=(u_1,,u_n). The first n-1 velocity field (u_1,, u_{n-1}) can be can be characterized by the classical $(n-1)$-dimensional Laplace equation;  while the last velocity u_n is linear; The pressure p and temperature \theta are  characterized by a generalized heat equation with variable coefficient. The technique used here is multi-dimensional.