On the uniqueness of solutions in the class of increasing functions of a system describing the dynamics of a viscous weakly stratified fluid in three dimensional space

We consider the Cauchy problem for a system of partial differential equations that describes the dynamics of a viscous weakly stratified fluid in three dimensional space. The existence of solutions of the problem follows from an explicit representation of the Fourier transform studied by the author in previous works. Here we prove the uniqueness of the weak solution of the problem in the class of growing functions.