Abstract.
The Cauchy problem for a nonlocal perturbation of KdV equation is considered by the Fourier restriction norm method. Local well-posedness for initial data in \(H^s({\mathbb{R}})(s > -\frac{3}{4})\) and global results for data in \(L^2({\mathbb{R}})\) are obtained.
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The first author was supported by the National Natural Science Foundation of China Grant No. 10601006.
The second author was supported by the National Natural Science Foundation of China Grant No.10526011.
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Huo, Z., Jia, Y. Low regularity solution for a nonlocal perturbation of KdV equation. Z. angew. Math. Phys. 59, 634–646 (2008). https://doi.org/10.1007/s00033-007-6086-y
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DOI: https://doi.org/10.1007/s00033-007-6086-y