Trevor Teolis : Well-posedness and long time behavior of the Euler Alignment System with adaptive communication strength

Posted by Christof Sparber , part of the Analysis and Applied Mathematics Seminar.

At

Feb. 5, 2024, 4 p.m.

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Abstract

We present a new flocking model which has the versatility to capture the physically realistic qualitative behavior of the Motsch-Tadmor model, while also retaining the entropy law, which lends to a similar 1D global well-posedness analysis to the Cucker-Smale model. This is an improvement to the situation in the Cucker-Smale case, which may display the physically unrealistic behavior that large flocks overpower the dynamics of small, far away flocks; and it is an improvement in the situation in the Motsch-Tadmor case, where 1D global well-posedness is not known. We discuss the general well-posedness theory for the new model and the long-time behavior including alignment, strong flocking in 1D, and entropy estimates to estimate the distribution of the limiting flock, all of which extend the classical results of the Cucker-Smale case. In addition, we provide numerical evidence to show the similar qualitative behavior between the new model and the Motsch-Tadmor model.