Characteristic exponents for a viscous fluid subjected to time dependent forces
The paper considers a viscous incompressible fluid enclosed in a bounded region of \({\mathbb{R}}^ 2\) or \({\mathbb{R}}^ 3\), and subjected to time dependent forces. The upper bounds on characteristic exponents, entropy and Hausdorff dimension for a time evolution described by nonlinear partial differential equations have been obtained. The original problem is decomposed into a linear and a nonlinear part. The linear problem is handled by use of existing methods. The nonlinear problem requires suitable a priori estimates. The method is likely to be useful in the study of dissipative physical systems.
upper bounds on characteristic exponents, entropy and Hausdorff dimension
scientific article; zbMATH DE number 3902250
scientific article