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On a Damped Szegö Equation (With an Appendix in Collaboration With Christian Klein)
SIAM Journal on Mathematical Analysis ( IF 2 ) Pub Date : 2020-09-17 , DOI: 10.1137/19m1299189 Patrick Gérard , Sandrine Grellier
SIAM Journal on Mathematical Analysis ( IF 2 ) Pub Date : 2020-09-17 , DOI: 10.1137/19m1299189 Patrick Gérard , Sandrine Grellier
SIAM Journal on Mathematical Analysis, Volume 52, Issue 5, Page 4391-4420, January 2020.
We investigate how damping the lowest Fourier mode modifies the dynamics of the cubic Szegö equation. We show that there is a nonempty open subset of initial data generating trajectories with high Sobolev norms tending to infinity. In addition, we give a complete picture of this phenomenon on a reduced phase space of dimension $6$. An appendix is devoted to numerical simulations supporting the generalization of this picture to more general initial data.
中文翻译:
关于阻尼的Szegö方程(与Christian Klein合作附录)
SIAM数学分析期刊,第52卷,第5期,第4391-4420页,2020年1月。
我们研究了最低傅立叶模态的阻尼如何改变三次Szegö方程的动力学。我们表明,有高Sobolev范数趋于无穷大的初始数据生成轨迹的非空开放子集。另外,我们给出了在尺寸为$ 6 $的减小的相空间上这种现象的完整描述。附录专门用于数值模拟,以支持将该图片推广为更通用的初始数据。
更新日期:2020-09-20
We investigate how damping the lowest Fourier mode modifies the dynamics of the cubic Szegö equation. We show that there is a nonempty open subset of initial data generating trajectories with high Sobolev norms tending to infinity. In addition, we give a complete picture of this phenomenon on a reduced phase space of dimension $6$. An appendix is devoted to numerical simulations supporting the generalization of this picture to more general initial data.
中文翻译:
关于阻尼的Szegö方程(与Christian Klein合作附录)
SIAM数学分析期刊,第52卷,第5期,第4391-4420页,2020年1月。
我们研究了最低傅立叶模态的阻尼如何改变三次Szegö方程的动力学。我们表明,有高Sobolev范数趋于无穷大的初始数据生成轨迹的非空开放子集。另外,我们给出了在尺寸为$ 6 $的减小的相空间上这种现象的完整描述。附录专门用于数值模拟,以支持将该图片推广为更通用的初始数据。