On the Weyl decomposition of the space $$\mathop D\limits^ \circ \left( \Omega \right)$$ and orthogonal projections of Navier-Stokes equationsand orthogonal projections of Navier-Stokes equations
Tóm tắt
The orthogonal decompositions
$$\mathop D\limits^ \circ = H \oplus P \oplus F, H \oplus P = H$$
, and
$$P \oplus F = F$$
are established, where
$$\mathop D\limits^ \circ $$
is an energetic Hilbert space over some open (not necessarily bounded) domain with piecewise smooth boundary in two- or three-dimensional Euclidean space. An intrinsic characterization of the subspacesH, P andF is given as well.
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