Journal article
LOCAL EXISTENCE THEORY FOR DERIVATIVE NONLINEAR SCHRODINGER EQUATIONS WITH NONINTEGER POWER NONLINEARITIES
SIAM journal on mathematical analysis, v 47(3), pp 2241-2264
01 Jan 2015
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Abstract
We study a derivative nonlinear Schrodinger equation, allowing noninteger powers in the nonlinearity, vertical bar u vertical bar(2 sigma)u(x). Our main theorem is short-time existence of solutions with initial data in the energy space, H-1; this is achieved by a careful use of the energy method. For more regular initial data, we establish not just the existence of solutions but also the well-posedness of the initial value problem. These results hold for real-valued sigma >= 1, while prior existence results in the literature require integer-valued sigma or sigma sufficiently large (sigma >= 5/2), use higher-regularity function spaces, or impose a smallness condition on the initial data.
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Details
- Title
- LOCAL EXISTENCE THEORY FOR DERIVATIVE NONLINEAR SCHRODINGER EQUATIONS WITH NONINTEGER POWER NONLINEARITIES
- Creators
- David M. Ambrose - Drexel UniversityGideon Simpson - Drexel University
- Publication Details
- SIAM journal on mathematical analysis, v 47(3), pp 2241-2264
- Publisher
- Siam Publications
- Number of pages
- 24
- Grant note
- DMS-1008387; DMS-1016267; DMS-1409018 / National Science Foundation; National Science Foundation (NSF) 1409018 / Division Of Mathematical Sciences; National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000357408600021
- Scopus ID
- 2-s2.0-84940386316
- Other Identifier
- 991019168615204721
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- Web of Science research areas
- Mathematics, Applied