Lower bounds on mixing norms for the advection diffusion equation in Rd

被引：0

作者：

Nobili, Camilla ^{[1
]}

Pottel, Steffen ^{[2
]}

机构：

[1] Univ Hamburg, Dept Math, D-20146 Hamburg, Germany

[2] Kuhne Logist Univ, D-20457 Hamburg, Germany

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2022年 / 29卷 / 02期

关键词：

Advection-Diffusion; Fourier splitting; Decay character; Passive scalar mixing; LARGE TIME BEHAVIOR; CONVECTION-ENHANCED DIFFUSION; DECAY CHARACTERIZATION;

D O I：

10.1007/s00030-021-00744-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An algebraic lower bound on the energy decay for solutions of the advection-diffusion equation in R-d with d = 2,3 is derived using the Fourier-splitting method. Motivated by a conjecture on mixing of passive scalars in fluids, a lower bound on the L-2- norm of the inverse gradient of the solution is obtained via gradient estimates and interpolation.

引用

页数：32

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