Selected papers of the 8th international school on mathematical theory in fluid mechanics, Paseky, Czech Republic, June 2003 (original) (raw)

New Directions in Mathematical Fluid Mechanics

New Directions in Mathematical Fluid Mechanics, 2020

Mechanics is a forum for the publication of high quality monographs, or collections of works, on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. Its mathematical aims and scope are similar to those of the Journal of Mathematical Fluid Mechanics. In particular, mathematical aspects of computational methods and of applications to science and engineering are welcome as an important part of the theory. So also are works in related areas of mathematics that have a direct bearing on fluid mechanics.

Progress in Mathematical Fluid Dynamics

2020

The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

International Winter School on Mathematical Fluid Dynamics

2012

M.V. Bartuccelli: Explicit estimates for the L∞-norm of solutions of the two-dimensional Navier-Stokes equations on the torus Abstract: Differential and integral inequalities are a basic tool in the study of the solutions of nonlinear partial differential equations (PDEs). With some exceptions, the constants on which they depend are not commonly computed explicitly. This does not present a problem in some context such as in attempting to prove regularity for the three-dimensional Navier-Stokes equations. Nevertheless, in other situations the estimation of constants is very important as they often contain geometric and number theoretic information which shed light on the overall significance and power of the inequalities themselves. In addition, knowledge of these constants can be crucial for a sharp and detailed analysis of the solutions of PDEs. In this talk we provide explicit (and accurate) values for the constants appearing in the functional estimates of the solutions of the two...

International Research Training Group 1529 Mathematical Fluid Dynamics

2014

A sort of continuous dependance on data for a suitable weak solution to the Navier-Stokes Cauchy problem 17:15-17:40 M. Kyed Weak time-periodic solutions to the Navier-Stokes equations in the three-dimensional wholespace with a non-zero drift term: Asymptotic profile at spatial infinity 17:45-18:10 W. Varnhorn On the non-homogeneous Navier-Stokes equations 18:30-21:00 RECEPTION

Physical and Mathematical Fluid Mechanics

Water

Fluid mechanics has emerged as a basic concept for nearly every field of technology. Despite there being a well-developed mathematical theory and available commercial software codes, the computation of solutions of the governing equations of motion is still challenging, especially due to the nonlinearity involved, and there are still open questions regarding the underlying physics of fluid flow, especially with respect to the continuum hypothesis and thermodynamic local equilibrium. The aim of this Special Issue is to reference recent advances in the field of fluid mechanics both in terms of developing sophisticated mathematical methods for finding solutions of the equations of motion, on the one hand, and on novel approaches to the physical modelling beyond the continuum hypothesis and thermodynamic local equilibrium, on the other.

Lecture Notes on Fluid Dynamics (1.63J/2.21J)

2002

Lecture Notes on Fluid Dynamics (1.63J/2.21J) by Chiang C. Mei, 2007 5.2 Kelvin-Helmholtz instability of flow with discontinuous shear and stratification. 5.2.1 Nonlinear formulation Consider two immiscible fluids. The upper (z > 0) and lower (z < 0) fluids have different densities ρ 1 and ρ 2. Before any perturbations appear the lower fluid is stationary, while the upper fluid moves at the steady and uniform velocityq o = U i. With gravity, this is called the Kelvin-Helmholtz instability problem. For the time being, let us assume that there is no gravity. Now let there be a disturbance on the interface whose vertical displacement is z = ζ(x, t). The corresponding disturbances of velocity and pressure are q 1 and p 1 in the upper fluid and q 2 and p 2 in the lower fluid. Let us first formulate the nonlinear problem. In the upper fluid, we have