Global solvability of the multidimensional equations of compressible non-Newtonian fluids, transport equation and the Orlicz spaces

The article illustrates the application of the theory of the Orlicz spaces in global solvability of boundary value problems for the equations of multidimensional flows of viscous compressible fluids and for the transport equation. While solving the main problem, a new method of extrapolation from the scale of the Lebesgue spaces into the Orlicz spaces is developed basing on integral representations and transforms of $N$-functions. The efficiency of the extrapolation method developed here is illustrated by the uniqueness problem for the Euler equations. A wide review of known results is given wherever necessary.