Tohoku Mathematical Journal
2021

March
SECOND SERIES VOL. 73, NO. 1

Tohoku Math. J.
73 (2021), 49-98

Title GLOBAL EXISTENCE OF SMALL SOLUTIONS FOR A QUADRATIC NONLINEAR FOURTH-ORDER SCHRÖDINGER EQUATION IN SIX SPACE DIMENSIONS

Author Kazuki Aoki

(Received September 5, 2019, revised November 21, 2019)
Abstract. We consider the Cauchy problem for the nonlinear fourth-order Schrödinger equation in six space dimensions with a quadratic nonlinearity. We prove a global existence and time decay estimates of solutions if the data are small, regular and decay rapidly at infinity.

Mathematics Subject Classification. Primary 35Q55.

Key words and phrases. Fourth-order nonlinear Schrödinger equation, global existence, the normal form method.

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