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- W2055893158 abstract "We consider the Cauchy problem associated to the generalized Benjamin-Bona-Mahony (BBM) equation for given data in the $L^2$-based Sobolev spaces. Depending on the order of nonlinearity and dispersion, we prove that the Cauchy problem is ill-posed for data with lower order Sobolev regularity. We also prove that, in certain range of the Sobolev regularity, even if the solution exists globally in time, it fails to be smooth." @default.
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- W2055893158 date "2014-05-01" @default.
- W2055893158 modified "2023-10-11" @default.
- W2055893158 title "On ill-posedness for the generalized BBM equation" @default.
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- W2055893158 doi "https://doi.org/10.3934/dcds.2014.34.4565" @default.
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