Global Results for Weakly Dispersive KP-II Equations on the Cylinder

Abstract We consider the dispersion-generalized KP-II equation on a partially periodic domain in the weakly dispersive regime. We use Fourier decoupling techniques to derive essentially sharp Strichartz estimates. With these in hand, we show that global well-posedness of the quasilinear Cauchy problem in $$L^2(\mathbb {R}\times \mathbb {T})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>×</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . Finally, we prove a long-time decay property of solutions with small mass by using the Kato smoothing effect in the fractional case.