Global solvability of the multidimensional equations of compressible non-Newtonian fluids, transport equation and the Orlicz spaces. (Russian. English summary) Zbl 1299.76213
Summary: 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.
MSC:
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 35F10 | Initial value problems for linear first-order PDEs |
| 44A35 | Convolution as an integral transform |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
