Resumen de Unconditional uniqueness for the modified Korteweg–de Vries equation on the line

Luc Molinet, Didier Pilod, Stéphane Vento

• We prove that the modified Korteweg–de Vries (mKdV) equation is unconditionally well-posed in Hs(R) for s>1/3. Our method of proof combines the improvement of the energy method introduced recently by the first and third authors with the construction of a modified energy. Our approach also yields a priori estimates for the solutions of mKdV in Hs(R), for s>0, and enables us to construct weak solutions at this level of regularity.