- Turkish Journal of Mathematics
- Vol: 42 Issue: 4
- Accelerating diffusion by incompressible drift on the two-dimensional torus
Accelerating diffusion by incompressible drift on the two-dimensional torus
Authors : Yaakoubi Nejib
Pages : 1877-1886
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Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :In this paper we construct an explicit sequence of divergence-free vector fields $\rm{b}_{n}$ that pushes the spectral gap of the nonself-adjoint operator $A_{\rm{b}_{n}}=\Delta +\rm{b}_{n}\cdot\nabla $ to infinity. The spectral gap is an indicator for the speed at which this diffusion converges toward its equilibrium, which corresponds to the uniform distribution.Keywords : Nonself-adjoint operator, spectral gap, divergence-free vector fields, rearrangement, comparison manifold, Faber-Krahn inequality