A-priori estimates for generalized Korteweg-de Vries equations in $H^{-1}(\mathbb{R})$

Mihaela Ifrim, Thierry Laurens

We prove local-in-time a-priori estimates in $H^{-1}(\mathbb{R})$ for a family of generalized Korteweg--de Vries equations. This is the first estimate for any non-integrable pertur…