Abstract
We propose a model of a density-dependent compressible-incompressible fluid, which is intended as a simplified version of models based on mixture theory as, for instance, those arising in the study of biofilms, tumor growth and vasculogenesis. Though our model is, in some sense, close to the density-dependent incompressible Euler equations, it presents some differences that require a different approach from an analytical point of view. In this paper, we establish a result of local existence and uniqueness of solutions in Sobolev spaces to our model, using the Leray projector. Besides, we show the convergence of both a continuous version of the Chorin-Temam projection method, viewed as a singular perturbation approximation, and the artificial compressibility method.
Anno
2017
Autori IAC
Tipo pubblicazione
Altri Autori
Bianchini, Roberta; Natalini, Roberto
Editore
World Scientific,
Rivista
Journal of hyperbolic differential equations