CAUCHY PROBLEM FOR THE ZAKHAROV SYSTEM ARISING FROM ION-ACOUSTIC MODES WITH LOW REGULARITY DATA

Boling Guo; Lijia Han; Zaihui Gan

doi:10.11948/2012002

2012 Volume 2 Issue 1

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Boling Guo, Lijia Han, Zaihui Gan. CAUCHY PROBLEM FOR THE ZAKHAROV SYSTEM ARISING FROM ION-ACOUSTIC MODES WITH LOW REGULARITY DATA[J]. Journal of Applied Analysis & Computation, 2012, 2(1): 11-28. doi: 10.11948/2012002

Citation:

Boling Guo, Lijia Han, Zaihui Gan. CAUCHY PROBLEM FOR THE ZAKHAROV SYSTEM ARISING FROM ION-ACOUSTIC MODES WITH LOW REGULARITY DATA[J]. Journal of Applied Analysis & Computation, 2012, 2(1): 11-28. doi: 10.11948/2012002

CAUCHY PROBLEM FOR THE ZAKHAROV SYSTEM ARISING FROM ION-ACOUSTIC MODES WITH LOW REGULARITY DATA

1 Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, China;
2 Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China;
3 College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, China

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Abstract

Abstract

We prove local well-posedness results for the Zakharov System Arising from Ion-Acoustic Modes in two spacial dimension with large initial data in low regularity Sobolev space (Ḣ∪H^1/2)×L²×H^-1. Using "derivative sharing", the local well-posedness results in (Ḣ∪H^1/2-δ)×H^δ×H^-1+δ are also obtained, for any 0 ≤ δ ≤ 1/2.
- Zakharov System /
- Bourgain space /
- Cauchy problem /
- Local wellposedness
MSC: 35Q55;35L70

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