We prove global existence of H2 solutions to the Cauchy problem for the generalized derivative nonlinear Schr\"odinger equation on the 1-d torus. This answers an open problem posed by Ambrose and Simpson [D. M. Ambrose and G. Simpson, SIAM J. Math. Anal., 47 (2015), pp. 2241-2264]. The key is the extraction of the terms that cause the problem in energy estimates and the construction of suitable energies so as to cancel the problematic terms out by effectively using integration by parts and the equation.
GLOBAL H2-SOLUTIONS FOR THE GENERALIZED DERIVATIVE NLS ON T
Hayashi M.;Ozawa T.;Visciglia N.
2025-01-01
Abstract
We prove global existence of H2 solutions to the Cauchy problem for the generalized derivative nonlinear Schr\"odinger equation on the 1-d torus. This answers an open problem posed by Ambrose and Simpson [D. M. Ambrose and G. Simpson, SIAM J. Math. Anal., 47 (2015), pp. 2241-2264]. The key is the extraction of the terms that cause the problem in energy estimates and the construction of suitable energies so as to cancel the problematic terms out by effectively using integration by parts and the equation.File in questo prodotto:
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