Author:
Osawa Satoshi,Takaoka Hideo
Abstract
We study the global well-posedness of the Zakharov-Kuznetsov equation on cylindrical spaces. Our goal is to establish the existence of global-in-time solutions below the energy class. To prove the results, we adapt the I-method to extend the local solutions globally in time. The main tool in our argument is multilinear estimates in the content of Bourgain's spaces. Using modified energies induced
For more information see https://ejde.math.txstate.edu/Volumes/2024/05/abstr.html
Reference26 articles.
1. C. Albarracin, G. R. Blanco; The IVP for a periodic generalized ZK equation, J. Differ. Equ., 352 (2023), 122.
2. J. Bourgain; Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, Part I: Schršodinger equations, Geom. Funct. Anal., 3 (1993), 107156.
3. J. Bourgain; Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, Part II: The KdV equation, Geom. Funct. Anal., 3 (1993), 209262.
4. T. J. Bridges; Universal geometric condition for the transverse instability of solitary waves, Phys. Rev. Lett., 84 (2000), 26142617.
5. J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao; Global well-posedness for KdV in Sobolev spaces of negative index, Electron. J. Differ. Equ., 2001 26 (2001), 17.