Tadahiro Oh
Abstract:
We consider the global well-posedness problem of a one-parameter
family of coupled KdV-type systems both in the periodic and non-periodic
setting. When the coupling parameter
,
we prove the global
well-posedness in
for
and
for
via the I-method developed
by Colliander-Keel-Staffilani-Takaoka-Tao [5].
When
,
as in the local theory [14],
certain resonances occur, closely depending on the value of
.
We use the Diophantine conditions to characterize the resonances.
Then, via the second iteration of the I-method, we establish a
global well-posedness result in
,
,
where
is determined by the
Diophantine characterization of certain constants derived from the
coupling parameter
.
We also show that the third iteration of
the I-method fails in this case.
Submitted August 2, 2008. Published April 14, 2009.
Math Subject Classifications: 35Q53.
Key Words: KdV; global well-posedness; I-method; Diophantine condition.
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Tadahiro Oh Department of Mathematics, University of Toronto 40 St. George St, Rm 6290 Toronto, ON M5S 2E4, Canada email: oh@math.toronto.edu |
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