Solutions to the Korteweg–de Vries Equation with Initial Profile in $L_1^1 (mathbb{R}) cap L_N^1 (mathbb{R}^ + )$
- 1 July 1987
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 18 (4) , 991-1025
- https://doi.org/10.1137/0518076
Abstract
The Cauchy problem for the Korteweg–de Vries equation is considered with initial profile integrable against $(1 + | x |)dx$ on $mathbb{R}$ and against $(1 + | x |)^N dx$ on $mathbb{R}^ + $. Classical solutions are constructed for $N geqq {{11} / 4}$. Under mild additional hypotheses the solution evolves in $L^2 (mathbb{R})$.
Keywords
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