Global existence and uniqueness result for the diffusive Peterlin viscoelastic model

Abstract The aim of this paper is to present the existence and uniqueness result for the diffusive Peterlin viscoelastic model describing the unsteady behaviour of some incompressible polymeric fluids. The polymers are treated as two beads connected by a nonlinear spring. The Peterlin approximation of the spring force is used to derive the equation for the conformation tensor. The latter is the time evolution equation with spatial diffusion of the conformation tensor. Using the energy estimates we prove global in time existence of a weak solution in two space dimensions. We are also able to show the regularity and consequently the uniqueness of the weak solution.

Computing oscillatory solutions of the Euler system via 𝒦-convergence

We develop a method to compute effectively the Young measures associated to sequences of numerical solutions of the compressible Euler system. Our approach is based on the concept of [Formula: see text]-convergence adapted to sequences of parameterized measures. The convergence is strong in space and time (a.e. pointwise or in certain [Formula: see text] spaces) whereas the measures converge narrowly or in the Wasserstein distance to the corresponding limit.

Energy dissipative characteristic schemes for the diffusive Oldroyd-B viscoelastic fluid