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On growth of Sobolev norms for energy critical NLS on irrational tori: small energy case. (English) Zbl 1409.35190

Summary: We consider the energy-critical nonlinear Schrödinger equation on a generic irrational torus \(\mathbb{T}_\lambda^3\). Using the long-time Strichartz estimates proved in [the author et al., “Long time Strichartz estimates on irrational tori”, Preprint], we establish polynomial upper bounds for higher Sobolev norms for solutions with small energy.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
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