270 research outputs found
Stability of a coupled wave-Klein-Gordon system with quadratic nonlinearities
Using the hyperboloidal foliation method, we establish stability results for
a coupled wave-Klein-Gordon system with quadratic nonlinearities. In
particular, we investigate quadratic wave-Klein-Gordon interactions in which
there are no derivatives on the massless wave component. By combining
hyperboloidal energy estimates with appropriate transformations of our fields,
we are able to show global existence of solutions for sufficiently small
initial data.Comment: Published version. Both authors are grateful to the anonymous
referees, whose comments improve a lot on the presentation and the precision
of the articl
Asymptotic stability for the Dirac--Klein-Gordon system in two space dimensions
We study the Dirac--Klein-Gordon system in spacetime dimensions. We
show global existence of the solutions, as well as sharp time decay and linear
scattering. One key advance is that we provide the first asymptotic stability
result for the Dirac--Klein-Gordon system in spacetime dimensions in the
case of a massive Klein-Gordon field and a massless Dirac field. The
nonlinearities are below-critical in two spatial dimensions, and so our method
requires the identification of special structures within the system and novel
weighted energy estimates. Another key advance, is that our proof allows us to
weaken certain conditions on the nonlinear structures that have been assumed in
the literature.Comment: 37 page
Stability of some two dimensional wave maps: a wave--Klein-Gordon model
We are interested in the stability of a class of totally geodesic wave maps,
as recently studied by Abbrescia and Chen, and later by Duan and Ma. The
relevant equations of motion are a system of coupled semilinear wave and
Klein-Gordon equations in whose nonlinearities are critical
when . In this paper we use a pure energy method to show global existence
when . By carefully examining the structure of the nonlinear terms, we are
able to obtain uniform energy bounds at lower orders. This allows us to prove
pointwise decay estimates and also to reduce the required regularity.Comment: arXiv admin note: text overlap with arXiv:2011.1199
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