Contributions To Current Challenges In Mathematical Fluid Mechanics (Hardcover)

On Multidimensional Burgers Type Equations with Small Viscosity.- 1. Introduction.- 2. Upper estimates.- 3. Lower estimates.- 4. Fourier coefficients.- 5. Low bounds for spatial derivatives of solutions of the Navier Stokes system.- References.- On the Global Well-posedness and Stability of the Navier Stokes and the Related Equations.- 1. Introduction.- 2. Littlewood Paley decomposition.- 3. Proof of Theorems.- References.- The Commutation Error of the Space Averaged Navier Stokes Equations on a Bounded Domain.- 1. Introduction.- 2. The space averaged Navier-Stokes equations in a bounded domain.- 3. The Gaussian filter.- 4. Error estimates in the (Lp(?d))d norm of the commutation error term.- 5. Error estimates in the (H-1(?))d norm of the commutation error term.- 6. Error estimates for a weak form of the commutation error term.- 7. The boundedness of the kinetic energy for n in some LES models.- References.- The Nonstationary Stokes and Navier Stokes Flows Through an Aperture.- 1. Introduction.- 2. Results.- 3. The Stokes resolvent for the half space.- 4. The Stokes resolvent.- 5. L4-Lr estimates of the Stokes semigroup.- 6. The Navier Stokes flow.- References.- Asymptotic Behavior at Infinity of Exterior Three-dimensional Steady Compressible Flow.- 1. Introduction.- 2. Function spaces and auxiliary results.- 3. Stokes and modified Stokes problems in weighted spaces.- 4. Transport equation and Poisson-type equation.- 5. Linearized problem.- 6. Nonlinear problem.- References.