On global well-posedness of the modified KdV equation in modulation spaces (Q2030856)

The Cauchy problem for the dispersive equation \(u_t+u_{xxx}\pm 6|u|^2u_x=0\) is studied in the, so-called, modulation spaces \(M^{r,p}_s(\mathbb R)\) more vast than the Fourier-Lebesgue spaces. If the threshold regularity exponent satisfies \(s\ge \frac14\) then the Cauchy problem with the initial data in \(M^{2,p}_s(\mathbb R)\), \(2\le p<\infty\) is locally and globally well posed.