التفاصيل البيبلوغرافية
| العنوان: |
Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity II: Dynamics. |
| المؤلفون: |
Bringmann, Bjoern1 bjoern@ias.edu |
| المصدر: |
Journal of the European Mathematical Society (EMS Publishing). 2024, Vol. 26 Issue 6, p1933-2089. 157p. |
| مصطلحات موضوعية: |
*GIBBS' equation, *WAVE equation, *NONLINEAR analysis, *MATHEMATICAL analysis, *DIFFERENTIAL equations |
| مستخلص: |
In this two-paper series, we prove the invariance of the Gibbs measure for a threedimensional wave equation with a Hartree nonlinearity. The novelty lies in the singularity of the Gibbs measure with respect to the Gaussian free field. In this paper, we focus on the dynamical aspects of our main result. The local theory is based on a paracontrolled approach, which combines ingredients from dispersive equations, harmonic analysis, and random matrix theory. The main contribution, however, lies in the global theory. We develop a new globalization argument, which addresses the singularity of the Gibbs measure and its consequences. [ABSTRACT FROM AUTHOR] |
| قاعدة البيانات: |
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