Well-Posedness for the Generalized Zakharov-Kuznetsov Equation on Modulation Spaces

作者：Kato Tomoya^*

来源：Journal of Fourier Analysis and Applications, 2017, 23(3): 612-655.

DOI：10.1007/s00041-016-9480-z

• Generalized Zakharov-Kuznetsov equation
• Global well-posedness
• Local well-posedness
• Modulation spaces

We consider the Cauchy problem for the generalized Zakharov-Kuznetzov equation on two or three space dimensions. We mainly study the two dimensional case and give the local well-posedness and the small data global well-posedness in the modulation space M-2,M-1(R-2) for m >= 4. Moreover, for the quartic case (namely, m = 3), the local well-posedness in M-2,1(1/4)(R-2) is given. The well-posedness on three dimensions is also considered.

• 出版日期2017-6