A-priori bounds for KdV equation below $H^{-3/4}$

Abstract

We consider the Korteweg-de Vries Equation (KdV) on the real line, and prove that the smooth solutions satisfy a-priori local in time $H^s$ bound in terms of the $H^s$ size of the initial data for $s\ge -4/5$.

References in corpus (2)

• The Korteweg-de-Vries equation at H^{-1} regularity
• Energy and local energy bounds for the 1-D cubic NLS equation in H^{-1/4}

Cited by in corpus (3)

• Conserved energies for the cubic NLS in 1-d
• On the uniqueness of solutions to the periodic 3D Gross-Pitaevskii hierarchy
• Low regularity bounds for mKdV