Hokkaido Mathematical Journal

Hokkaido Mathematical Journal, 36 (2007) pp.467-506

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Abstract

The Cauchy problem for a modified Zakharov system is proven to be locally well-posed for rough data in two and three space dimensions. In the three dimensional case the problem is globally well-posed for data with small energy. Under this assumption there also exists a global classical solution for sufficiently smooth data.

MSC(Primary) 35Q55 35L70 Zakharov system, well-posedness, Fourier restriction norm method