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arXiv · 1704.07027

Well-posedness of Weak and Strong Solutions to the Kinetic Cucker-Smale Model

Chunyin Jin
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Abstract

We first prove the well-posedness of weak and strong solutions to the kinetic Cucker-Smale model in the Sobolev space with the initial data having compact velocity support. Then we study the kinetic Cucker-Smale model with noise. By introducing two weighted Hilbert spaces, we successfully establish the well-posedness of weak and strong solutions, respectively. Our proof is based on weighted energy estimates. Finally, we rigorously justify the vanishing noise limit.

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Chunyin Jin. 2017-04-24. Well-posedness of Weak and Strong Solutions to the Kinetic Cucker-Smale Model. https://arxiv.org/abs/1704.07027

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