On the (generalized) Korteweg-de Vries equation
Copyright policy )On the (generalized) Korteweg-de Vries equation
The well-posedness of the initial value problem for the Korteweg-de Vries equation \(u_ t+ u_{xxx}+ uu_ x =0\) and its generalized form \(u_ t+ u_{xxx}+ a(u) u_ x=0\) in the classical Sobolev spaces and the regularity of their solutions in \(L_ s^ p\) spaces are studied. A global smoothing effect of the solutions of these equations is also proved. See also a paper by \textit{T. Kato} [Studies in applied mathematics, Adv. Math., Suppl. Stud., Vol. 8, 93-128 (1983; Zbl 0508.00010)].
35Q53, regularity, global smoothing, 35B65, KdV equations (Korteweg-de Vries equations), well-posedness, Smoothness and regularity of solutions to PDEs, Sobolev spaces, Korteweg-de Vries equation, initial value problem
35Q53, regularity, global smoothing, 35B65, KdV equations (Korteweg-de Vries equations), well-posedness, Smoothness and regularity of solutions to PDEs, Sobolev spaces, Korteweg-de Vries equation, initial value problem
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