Abtract：We consider on arbitrary Riemannian manifolds the Leibenson equation:$\partial _{t}u=\Delta _{p}u^{q}.$This equation comes from hydrodynamics where it describes filtration of a turbulent compressible liquid in porous medium. Here $u(x,t)$ is the fraction of the volume that the liquid takes in porous medium at time $t$ at point $x$. The parameter $p$ characterizes the turbulence of a...
摘要:We study emergent collective behaviors of a thermodynamic Cucker-Smale (TCS) ensemble on complete smooth Riemannian manifolds. For this, we extend the TCS model on the Euclidean space to a complete smooth Riemannian manifold by adopting the work for a CS ensemble and providing a sufficient framework to achieve velocity alignment and thermal equilibrium. Compared to the work for a CS ensemb...
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