arXiv subjects

Farah Abou Shakra

Publications and source records attributed to Farah Abou Shakra.

2 recordsLinked to original sources

arXiv2013

On 2D NLS on non-trapping exterior domains

Global existence and scattering for the nonlinear defocusing Schrödinger equation in 2 dimensions are known for domains exterior to star-shaped obstacles and for nonlinearities that grow at least as the quintic power. In this paper, we extend the global existence result for all non-trapping obstacles and for nonlinearities with power strictly greater than quartic. For such nonlinearities, we also prove scattering for a class of so-called almost star-shaped obstacles.

math.AP↗

arXiv2013

Asymptotics of the critical non-linear wave equation for a class of non star-shaped obstacles

Scattering for the energy critical non-linear wave equation for domains exterior to non trapping obstacles in 3+1 dimension is known for the star-shaped case. In this paper, we extend the scattering for a class of non star-shaped obstacles called illuminated from exterior. The main tool we use is the method of multipliers with weights that generalize the Morawetz multiplier to suit the geometry of the obstacle.

math.AP↗