带有非局部效应耦合流体模型的局部经典解
The Local Classical Solution of Coupled Fluid Model with Nonlocal Effect
DOI: 10.12677/PM.2021.114064, PDF,   
作者: 胡 烨, 佟丽宁：上海大学理学院数学系，上海
关键词: 非局部速度趋同；耦合；Nonlocal Velocity Alignment； Coupling
摘要: 本文研究了带有非局部速度趋同效应的耦合模型。该系统通过阻尼项对粒子速度和流体速度进行耦合，描述了群集粒子在粘性不可压流体中的相互作用。本文首先构造逼近方程和逼近解，并应用能量估计的方法，得到逼近解的一致先验估计，然后利用低阶范数收敛，证明具有非局部速度趋同效应的欧拉系统局部解的存在唯一性。
Abstract: This paper studied a coupling model with non-local velocity alignment. In this system, particle ve-locity and fluid velocity are coupled by damping term, and the interaction of cluster particles in viscous incompressible fluid is described. We first construct the approximation equation and the approximation solution, and the uniform a priori estimate of the approximation solution is obtained by using the method of energy coupling estimation, and then the existence and uniqueness of the local solution of the Euler system with non-local velocity convergence effect is proved by using the lower-order norm convergence.
文章引用：胡烨, 佟丽宁. 带有非局部效应耦合流体模型的局部经典解[J]. 理论数学, 2021, 11(4): 503-515. https://doi.org/10.12677/PM.2021.114064

参考文献

[1] Hauray, M. and Jabin, P.-E. (2007) N-Particles Approximation of the Vlasov Equations with Singular Potential. Archive for Rational Mechanics and Analysis, 183, 489-524.
[2] Cucker, F. and Smale, S. (2007) Emergent Behavior in Flocks. IEEE Transactions on Automatic Control, 52, 852-862. [Google Scholar] [CrossRef] 
[3] Etikyala, R., Gottlich, S., Klar, A. and Tiwari, S. (2014) Particle Methods for Pedestrian Flow Models: From Microscopic to Nonlocal Continuum Models. Mathematical Models and Methods in Applied Sciences, 24, 2503-2523. [Google Scholar] [CrossRef] 
[4] Carrillo, J.A., Choi, Y.P. and Perez, S.P. (2017) A Review on Attractive-Repulsive Hydrodynamics for Consensus in Collective Behavior. In: Bellomo, N., Degond, P. and Tadmor, E., Eds., Active Particles, Volume 1, Birkhauser, Cham, 259-298. [Google Scholar] [CrossRef] 
[5] Carrillo, J.A., Fornasier, M., Toscani, G. and Vecil, F. (2010) Particle, Kinetic, and Hydrodynamic Models of Swarming. In: Naldi, G., Pareschi, L. and Toscani, G., Eds., Mathemat-ical Modeling of Collective Behavior in Socio-Economic and Life Sciences, Birkhauser, Boston, 297-336. [Google Scholar] [CrossRef] 
[6] Che, J., Chen, L., Göttlich, S. and Wang, J. (2016) Existence of a Classical Solution to Complex Material Flow Problems. Mathematical Methods in the Applied Sciences, 39, 4069-4081. [Google Scholar] [CrossRef] 
[7] Carrillo, J.A., Choi, Y.P. and Zatorska, E. (2016) On the Pressureless Damped Euler-Poisson Equations with Quadratic Confinement: Critical Thresholds and Large-Time Be-havior. Mathematical Models and Methods in Applied Sciences, 26, 2311-2340. [Google Scholar] [CrossRef] 
[8] Carrillo, J.A., Choi, Y.P., Tadmor, E. and Tan, C. (2016) Crit-ical Thresholds in 1D Euler Equations with Non-Local Forces. Mathematical Models and Methods in Applied Sciences, 26, 185-206. [Google Scholar] [CrossRef] 
[9] Do, T., Kiselev, A., Ryzhik, L. and Tan, C. (2018) Global Regularity for the Fractional Euler Alignment System. Archive for Rational Mechanics and Analysis, 228, 1-37. [Google Scholar] [CrossRef] 
[10] Kiselev, A. and Tan, C. (2018) Global Regularity for 1D Eulerian Dynamics with Singular Interaction Forces. SIAM Journal on Mathematical Analysis, 50, 6208-6229. [Google Scholar] [CrossRef] 
[11] Carrillo, J.A., Feireisl, E., Gwiazda, P. and Swierczewska-Gwiazda, A. (2017) Weak Solutions for Euler System with Non-Local Interactions. Journal of the London Mathematical Society, 95, 705-724. [Google Scholar] [CrossRef] 
[12] Choi, Y.-P. (2019) The Global Cauchy Problem for Compressi-ble Euler Equations with a Nonlocal Dissipation. Mathematical Models and Methods in Applied Sciences, 29, 185-207.
[13] Carrillo, J.A., Wroblewska-Kaminska, A. and Zatorska, E. (2017) On Long-Time Asymptotics for Vis-cous Hydrodynamic Models of Collective Behavior with Damping and Nonlocal Interactions. Mathematical Models and Methods in Applied Sciences, 29, 31-63.
[14] Ha, S.Y., Kang, M.J. and Kwon, B. (2014) A Hydrodynamic Model for the Interaction of Cucker-Smale Particles and Incompressible Fluid. Mathematical Models and Methods in Applied Sciences, 24, 2311-2359. [Google Scholar] [CrossRef] 
[15] Kato, T. (1973) Linear Evolution Equations of “Hyperbolic” Type II. Journal of the Mathematical Society of Japan, 25, 648-666. [Google Scholar] [CrossRef] 
[16] Majda, A. (1984) Compressible Fluid Flowand Systems of Conserva-tion Laws in Several Space Variables. Applied Mathematical Sciences, Vol. 53. Springer-Verlag, New York. [Google Scholar] [CrossRef] 

为你推荐