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Global existence of small solutions to semilinear Schrödinger equations. (English) Zbl 0843.35111

Summary: We present global existence theorem for semilinear Schrödinger equations. In general, Schrödinger-type equations do not admit the classical energy estimates. To avoid this difficulty, we use S. Doi’s method for linear Schrödinger-type equations. Combining his method and \(L^p- L^q\) estimates, we prove the global existence of solutions with small initial data.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B45 A priori estimates in context of PDEs
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References:

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[9] DOI: 10.1016/0022-1236(92)90079-X · Zbl 0763.35077
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