On the well-posedness of the periodic KdV equation in high regularity classes

Kappeler, T; Pöschel, J (2008). On the well-posedness of the periodic KdV equation in high regularity classes. In: Craig, W. Hamiltonian dynamical systems and applications. Dordrecht: Springer, 431-441.

Abstract

We prove well-posedness results for the initial value problem of the periodic KdV equation in classes of high regularity solutions. More precisely, we consider the problem in weighted Sobolev spaces, which comprise classical Sobolev spaces, Gevrey spaces, and analytic spaces. We show that the initial value problem is well posed in all spaces with subexponential growth of Fourier coefficients, and ‘almost well posed’ in spaces with exponential growth of Fourier coefficients.

Abstract

We prove well-posedness results for the initial value problem of the periodic KdV equation in classes of high regularity solutions. More precisely, we consider the problem in weighted Sobolev spaces, which comprise classical Sobolev spaces, Gevrey spaces, and analytic spaces. We show that the initial value problem is well posed in all spaces with subexponential growth of Fourier coefficients, and ‘almost well posed’ in spaces with exponential growth of Fourier coefficients.

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