22,197 research outputs found
Sharp local well-posedness for the "good" Boussinesq equation
In the present article, we prove the sharp local well-posedness and
ill-posedness results for the "good" Boussinesq equation on ; the
initial value problem is locally well-posed in and
ill-posed in for . Well-posedness result is obtained
from reduction of the problem into a quadratic nonlinear Schr\"odinger equation
and the contraction argument in suitably modified spaces. The proof
of the crucial bilinear estimates in these spaces, especially in the lowest
regularity, rely on some bilinear estimates for one dimensional periodic
functions in spaces, which are generalization of the bilinear
refinement of the Strichartz estimate on . Our result
improves the known local well-posedness in with
given by Oh and Stefanov (2012) to the regularity threshold
. Similar ideas also establish the sharp local
well-posedness in and ill-posedness below for
the nonperiodic case, which improves the result of Tsugawa and the author
(2010) in with to the limiting regularity.Comment: 40 page
Some Properties of String Field Algebra
We examine string field algebra which is generated by star product in
Witten's string field theory including ghost part. We perform calculations
using oscillator representation consistently. We construct wedge like states in
ghost part and investigate algebras among them. As a by-product we have
obtained some solutions of vacuum string field theory. We also discuss some
problems about identity state. We hope these calculations will be useful for
further investigation of Witten type string field theory.Comment: 26 pages, typos corrected, v3:Eq.(92) corrected, v4:to be published
in JHE
Local well-posedness for the Zakharov system on multidimensional torus
The initial value problem of the Zakharov system on two dimensional torus
with general period is shown to be locally well-posed in the Sobolev spaces of
optimal regularity, including the energy space. Proof relies on a standard
iteration argument using the Bourgain norms. The same strategy is also
applicable to three and higher dimensional cases.Comment: 35 pages, 3 figure
UHF flows and the flip automorphism
A UHF flow is an infinite tensor product type action of the reals on a UHF
algebra and the flip automorphism is an automorphism of
sending into . If is an inner perturbation of
a UHF flow on , there is a sequence of unitaries in
such that converges to zero and the flip is
the limit of \Ad u_n. We consider here whether the converse holds or not and
solve it with an additional assumption: If and
absorbs any UHF flow (i.e., is cocycle conjugate
to ), then the converse holds; in this case is what we call a
universal UHF flow.Comment: 18 page
Resonant decomposition and the -method for the two-dimensional Zakharov system
The initial value problem of the Zakharov system on two-dimensional torus
with general period is considered in this paper. We apply the -method with
some 'resonant decomposition' to show global well-posedness results for
small-in- initial data belonging to some spaces weaker than the energy
class. We also consider an application of our ideas to the initial value
problem on and give an improvement of the best known result by
Pecher (2012).Comment: 29 page
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