51 research outputs found
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
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
Unconditional uniqueness for the periodic Benjamin-Ono equation by normal form approach
We show unconditional uniqueness of solutions to the Cauchy problem
associated with the Benjamin-Ono equation under the periodic boundary condition
with initial data given in for . This improves the previous
unconditional uniqueness result in by Molinet and Pilod (2012). Our
proof is based on a gauge transform and integration by parts in the time
variable.Comment: 19 page
- …