Well-posedness of the initial value problem for the Korteweg-de Vries equation

Carlos E. Kenig, Gustavo Ponce, Luis Vega

Type: Article

Publication Date: 1991-01-01

Citations: 607

DOI: https://doi.org/10.1090/s0894-0347-1991-1086966-0

Abstract

The conservation law ~k+2 ( .)provides an a priori estimate of the Hknorm (k = 0, 1, ... ) of a solution with data U o E Hk.Hence, combining the local result (s > 3/2), the invariants ~2 -~4' and some inequalities one obtains that the IVP (1.1) is globally well-posed in H S with s ~ 2 .

Locations

Journal of the American Mathematical Society - View - PDF

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