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- W2023174645 abstract "(1.1) &ItU + axu + U1xU = O, x, t E R { u(x, 0) = uo(x). The KdV equation, which was first derived as a model for unidirectional propagation of nonlinear dispersive long waves [21], has been considered in different contexts, namely in its relation with the inverse scattering method, in plasma physics, and in algebraic geometry (see [24], and references therein). Our purpose is to study local and global well-posedness of the IVP (1.1) in classical Sobolev spaces Hs(R) . We shall say that the IVP (1.1) is locally (resp. globally) well-posed in the function space X if it induces a dynamical system on X by generating a continuous local (resp. global) flow. It was established in the works of Bona and Smith [3], Bona and Scott [2], Saut and Temam [30], and Kato [ 1 5] that the IVP (1. 1) is locally (resp. globally) well-posed in Hs with s > 3/2 (resp. s > 2). Roughly speaking, global well-posedness in Hs depends on the available local theory and on the conservation laws satisfied by solutions of (1.1), namely:" @default.
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- W2023174645 date "1991-01-01" @default.
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- W2023174645 title "Well-posedness of the initial value problem for the Korteweg-de Vries equation" @default.
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