On the cubic NLS on 3D compact domains
2013 ◽
Vol 13
(1)
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pp. 1-18
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Keyword(s):
AbstractWe prove bilinear estimates for the Schrödinger equation on 3D domains, with Dirichlet boundary conditions. On non-trapping domains, they match the ${ \mathbb{R} }^{3} $ case, while on bounded domains they match the generic boundaryless manifold case. We obtain, as an application, global well-posedness for the defocusing cubic NLS for data in ${ H}_{0}^{s} (\Omega )$, $1\lt s\leq 3$, with $\Omega $ any bounded domain with smooth boundary.
2004 ◽
Vol 134
(1)
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pp. 69-87
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2011 ◽
Vol 55
(1)
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pp. 155-166
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2011 ◽
Vol 141
(6)
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pp. 1279-1294
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2002 ◽
Vol 74
(1-2)
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pp. 349-370
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2009 ◽
Vol 2009
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pp. 1-13
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