Journal article
Local Existence Theory for Derivative Nonlinear Schr\"{o}dinger Equations with Non-Integer Power Nonlinearities
27 Jan 2014
Abstract
We study a derivative nonlinear Schr\"{o}dinger equation, allowing
non-integer powers in the nonlinearity, $|u|^{2\sigma} u_x$. Making careful use
of the energy method, we are able to establish short-time existence of
solutions with initial data in the energy space, $H^1$. For more regular
initial data, we establish not just existence of solutions, but also
well-posedness of the initial value problem. These results hold for real-valued
$\sigma\geq 1,$ while prior existence results in the literature require
integer-valued $\sigma$ or $\sigma$ sufficiently large ($\sigma \geq 5/2$), or
use higher-regularity function spaces.
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Details
- Title
- Local Existence Theory for Derivative Nonlinear Schr\"{o}dinger Equations with Non-Integer Power Nonlinearities
- Creators
- David M AmbroseGideon Simpson
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Identifiers
- 991019295309604721