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Infinite gain of regularity for dispersive evolution equations. (English) Zbl 0767.35076
Microlocal analysis and nonlinear waves, Proc. Workshop, IMA Program Nonlinear Waves, Minneapolis/MN (USA) 1988-89, IMA Vol. Math. Appl. 30, 47-50 (1991).
[For the entire collection see Zbl 0758.00007.]
We divorce the question of regularity from the question of global existence. We succeed in proving the infinite gain of regularity within the existence interval for a general class of dispersive equations without any growth conditions on the nonlinear terms. We use a generalization of Kato’s original method, together with ideas of W. Craig and J. Goodman [J. Differ. Equations 87, No. 1, 38-61(1990; Zbl 0709.35090)].

35Q53 KdV equations (Korteweg-de Vries equations)
35B65 Smoothness and regularity of solutions to PDEs