We study properties of Lipschitz truncations of Sobolev functions with constant and variable exponent. As non-trivial applications we use the Lipschitz truncations to provide a simplified proof of an existence result for incompressible power-law like fluids presented in Frehse, Málek, Steinhauer: SIAM J. Math. Anal., 34, 1064-1083 (2003). We also establish new existence results to a class of in...

We address the system of partial differential equations modeling motion of an elastic body inside an incompressible fluid. The fluid is modeled by the incompressible Navier-Stokes equations while the structure is represented by the damped wave equation with interior damping. The additional boundary stabilization γ, considered in our previous paper, is no longer necessary. We prove the global ex...

Contents 1. Introduction 2 1.1. The Keyfitz and Kranzer system 2 1.2. Bressan's compactness conjecture 3 1.3. Ambrosio's renormalization Theorem 4 1.4. Well–posedness for the Keyfitz and Kranzer system 5 1.5. Renormalization conjecture for nearly incompressible BV fields 6 1.6. Plan of the paper 7 2. Preliminaries 8 2.1. Notation 8 2.2. Measure theory 9 2.3. Approximate continuity and approxima...

A~tract. The finite amplitude, coupled shear-torsional motion of a circular disk supported between identical rubber spring cylinders is studied. The material of the springs is assumed to be an incompressible elastic material. The oscillatory motion of the disk is studied for two different cases. In the first case, the material of the spring is assumed to be an incompressible elastic material wh...

Context: A visualization of three-dimensional incompressible flows by divergence-free quasitwo-dimensional projections of velocity field on three coordinate planes is proposed. Objective: To visualize 3D incompressible flow by 3 two-dimensional plots. Method: It is argued that such divergence-free projections satisfying all the velocity boundary conditions are unique for a given velocity field....

A general method for fluid solid interaction problem simulations has been developed in 3D algorithm using incompressible smoothed particle hydrodynamics (SPH) method. The solid is assumed to be rigid so it can be considered as moving boundaries for fluid. Using repulsive force has been proved to be an efficient boundary treatment for incompressible SPH method before with 2D examples. The advant...