We show that if the dispersion of the KdV equation is replaced by a higher order dispersion , where is an odd integer, then the critical Sobolev exponent for local well-posedness on the circle does not change. That is, the resulting equation is locally well-posed in , .
In this first talk, I will introduce the solution space for the IVP for KdV, state the lemmas, and state and prove the main theorem.
Keywords: KdV equation, Local well-posedness, Sobolev spaces, Fourier transform.
Well-posedness of KdV with higher dispersion - Part 1