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On the uniqueness of solutions to boundary value problems for non-stationary Euler equations. (English) Zbl 1195.35248

Fursikov, Andrei V. (ed.) et al., New directions in mathematical fluid mechanics. The Alexander V. Kazhikhov memorial volume. Boston, MA: Birkhäuser (ISBN 978-3-0346-0151-1/hbk). Advances in Mathematical Fluid Mechanics, 281-299 (2010).
Summary: We seek for extremely wide classes of generalized solutions to boundary value problems for nonsteady Euler equations where uniqueness still holds. Such classes appear to be formulated rather compactly in terms of the Orlicz spaces. This result is obtained with extrapolatory techniques in the scale of symmetric spaces which have been developed by the author based on integral representations and transforms of \(N\)-functions generating Orlicz spaces.
For the entire collection see [Zbl 1182.35002].

MSC:

35Q31 Euler equations
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
44A35 Convolution as an integral transform
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