Global bounded weak solutions to a degenerate quasilinear attraction–repulsion chemotaxis system with rotation

Global existence of solutions to a parabolic-elliptic chemotaxis system with critical degenerate di ffusion

Existence of at least three weak solutions for a quasilinear elliptic system

In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...

Global solutions to a chemotaxis system with non-diffusive memory

In this article, a existence theorem of global solutions with small initial data belonging to L ∩ L, (n < p ≤ ∞) for a chemotaxis system are given on the whole space R, n ≥ 3. In the case p = ∞, our global solution is integrable with respect to the space variable on some time interval, and then conserves the mass for a short time, at least. The system consists of a chemotaxis equation with a lo...

Global weak solutions for a degenerate parabolic system modeling the spreading of insoluble surfactant

It is a widely used approach in the study of the dynamical behavior of viscous thin films to approximate the full fluid mechanical system by simpler model equations, using e.g. lubrication theory and cross-sectional averaging. In most of such models surface tension effects may then become significant, or even dominant. Therefore, also the influence of surfactant, i.e. surface active agents on t...

Global weak solutions for SQG in bounded domains

We prove existence of global weak L solutions of the inviscid SQG equation in bounded domains.