Existence and positivity of a system k-ε with a production term of the Rayleigh-Taylor type

Analysis of a turbulence model related to that of k-epsilon for stationary and compressible flows

“…Hence our analysis can handle compressible turbulent flows. The condition of the form (20) assumed for div u is much weaker than the corresponding assumption made in [15]. In dimension two, under the additional condition (A 1 ) we obtain in theorem 2 an existence result without any additional assumption of low compressibility.…”

“…Then the balance between the increase/decrease of the source terms of turbulence and the possible explosion/vanishing of the turbulent viscosities is difficult to control. Compared to previous works (see [16,15,23,28]) our basic assumption (A 0 ) made in theorem 1 is very general, and we remark that: i) We do not impose a free divergence condition on u and the mean density ρ is not supposed constant. Hence our analysis can handle compressible turbulent flows.…”

Analysis of a Singular Convection Diffusion System Arising in Turbulence Modelling

“…Compared to previous works (see [1,7,12,13]) our basic assumption ( 0 ) made in Theorem 1 is very general. In particular, we do not artificially cancel the singularity in the model, and we only assume weak regularity on the data.…”