Abstract.
We prove the global well-posedness of the KP-I equation in \({\Bbb R}^2\) for data of arbitrary size in a suitable Sobolev class. We use a compactness method to get local solutions. We extend the solutions thanks to some conservation laws, an almost conserved quantity and Strichartz estimates.
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Received: 5 April 2001 / Revised version: 22 October 2001 / Published online: 17 June 2002
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Molinet, L., Saut, J. & Tzvetkov, N. Global well-posedness for the KP-I equation. Math Ann 324, 255–275 (2002). https://doi.org/10.1007/s00208-002-0338-0
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DOI: https://doi.org/10.1007/s00208-002-0338-0