We consider the single layer potential associated to the fundamental solution of the time-dependent Oseen system. It is shown this potential belongs to L²(0,∞,H¹(Ω)³) and to H¹(0,∞,V') if the layer function is in L²(∂Ω×(0,∞)³). (Ω denotes the complement of a bounded Lipschitz set; V denotes the set of smooth solenoidal functions in H¹₀(Ω)³.) This result means that the usual weak solution of the time-dependent Oseen function with zero initial data and zero body force may be represented by a single layer potential, provided a certain integral equation involving the boundary data may be solved.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-8,
author = {Paul Deuring},
title = {On boundary-driven time-dependent Oseen flows},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {119-132},
zbl = {1148.76016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-8}
}
Paul Deuring. On boundary-driven time-dependent Oseen flows. Banach Center Publications, Tome 83 (2008) pp. 119-132. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-8/