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- W2950240173 abstract "We complete the known results on the local Cauchy problem in Sobolev spaces for the KdV-Burgers equation by proving that this equation is well-posed in $ H^{-1}(R) $ with a solution-map that is analytic from $H^{-1}(R) $ to $C([0,T];H^{-1}(R))$ whereas it is ill-posed in $ H^s(R) $, as soon as $ s 0 $ small enough. As far as we know, this is the first result of this type for a dispersive-dissipative equation. The framework we develop here should be very useful to prove similar results for other dispersive-dissipative models" @default.
- W2950240173 created "2019-06-27" @default.
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- W2950240173 date "2011-01-01" @default.
- W2950240173 modified "2023-10-06" @default.
- W2950240173 title "Sharp ill-posedness and well-posedness results for the KdV-Burgers equation: the real line case" @default.
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