Dissipative weak solutions to compressible Navier–Stokes–Fokker–Planck systems with variable viscosity coefficients

Viscosity Solutions and Computation for Dissipative Systems

Recent activity in nonlinear H∞ control has sparked renewed interest in the theory of dissipative nonlinear systems. This theory was initiated byWillems (1972) and developed further by Hill & Moylan (1976). Central to this theory are the so-called storage functions. These functions are generalized energy functions defined in terms of dissipation inequalities. The natural infinitesimal versions ...

From Suitable Weak Solutions to Entropy Viscosity

This paper focuses on the notion of suitable weak solutions for the three-dimensional incompressible Navier–Stokes equations and discusses the relevance of this notion to Computational Fluid Dynamics. The purpose of the paper is twofold (i) to recall basic mathematical properties of the three-dimensional incompressible Navier-Stokes equations and to show how they relate to LES (ii) to introduce...

Weighted L-estimates for Dissipative Wave Equations with Variable Coefficients

We establish weighted L2-estimates for the wave equation with variable damping utt −∆u+ aut = 0 in R, where a(x) ≥ a0(1+ |x|)−α with a0 > 0 and α ∈ [0, 1). In particular, we show that the energy of solutions decays at a polynomial rate t−(n−α)/(2−α)−1 if a(x) ∼ a0|x|−α for large |x|. We derive these results by strengthening significantly the multiplier method. This approach can be adapted to ot...

Exact Solutions to a Generalized BBM Equation with Variable Coefficients

An auxiliary equation technique is applied to investigate a generalized Benjamin-Bona-Mahony equation with variable coefficients. Many exact traveling wave solutions are obtained which include algebraic solutions, solitons, solitary wave solutions and trigonometric solutions. Mathematics Subject Classification: 35Q53, 35B35

Remarks on Fundamental Solutions to Schrödinger Equation with Variable Coefficients