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J. Korean Math. Soc. 2001; 38(6): 1205-1234

Printed November 1, 2001

Copyright © The Korean Mathematical Society.

Well-posedness for the Benjamin equations

Hideo Kozono, Takayoshi Ogawa, and Hirooki Tanisaka

Tohoku University, Kyushu University, Tohoku University

Abstract

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We consider the time local well-posedness of the Benjamin equation. Like the result due to Kenig-Ponce-Vega [10], [12], we show that the initial value problem is time locally well posed in the Sobolev space $H^s(\mathbb R)$ for $s > - 3/4$.

Keywords: Benjamin equation, local well-posedness, initial value problem, KdV equation

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