Global well-posedness for low regularity data in the 2d modified Zakharov-Kuznetsov equation

Abstract

We consider the modified Zakharov-Kuznetsov (mZK) equation in two space dimensions in both focusing and defocusing cases. Using the $I$-method, we prove the global well-posedness of the $H^s$ solutions for $s>\frac{3}{4}$ for any data in the defocusing case and under the assumption that the mass of the initial data is less than the mass of the ground state solution of $\Delta \phi -\phi +{\phi }^3=0$ in the focusing case. This improves the global well-posedness result of Linares and Pastor [20].

29 pages

References in corpus (1)

• Blow-up in finite or infinite time of the 2D cubic Zakharov-Kuznetsov equation

Cited by in corpus (5)

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• Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation
• Asymptotic K-soliton-like Solutions of the Zakharov-Kuznetsov type equations
• Dispersive Blow-up for Solutions of the Zakharov-Kuznetsov equation
• The Cauchy problem for the $L^2-$critical generalized Zakharov-Kuznetsov equation in dimension 3