Quantitative local sensitivity estimates for the random kinetic Cucker-Smale model with chemotactic movement

Seung-Yeal Ha; Bora Moon

doi:10.3934/krm.2020031

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2020, Volume 13, Issue 5: 889-931. Doi: 10.3934/krm.2020031

This issue Previous Article Kinetic formulation of a 2 × 2 hyperbolic system arising in gas chromatography Next Article On the transport operators arising from linearizing the Vlasov-Poisson or Einstein-Vlasov system about isotropic steady states

Quantitative local sensitivity estimates for the random kinetic Cucker-Smale model with chemotactic movement

Seung-Yeal Ha^1,2, and
Bora Moon^3, ,

1.
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 08826
2.
Korea Institute for Advanced Study, Hoegiro 85, Seoul, 02455, Republic of Korea
3.
Department of Mathematical Sciences, Seoul National University, Seoul 08826, Republic of Korea

^* Corresponding author: Bora Moon
^* Corresponding author: Bora Moon

Received: November 2019

Revised: March 2020

Published: August 2020

The work of S.-Y. Ha was supported by the NRF grant (2017R1A2B2001864) and the work of B. Moon was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (2019R1I1A1A01059585)

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Abstract

In this paper, we present quantitative local sensitivity estimates for the kinetic chemotaxis Cucker-Smale(CCS) equation with random inputs. In the absence of random inputs, the kinetic CCS model exhibits velocity alignment under suitable structural assumptions on the turning kernel and reaction term despite of the random effect due to a turning operator. We provide a global existence of a regular solution with slow velocity alignment for the random kinetic CCS model within the proposed framework. Moreover, we investigate the propagation of regularity and stability of infinitesimal variations in random space.

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Mathematics Subject Classification: Primary: 35Q82, 35Q92, 37H99.

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