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Piotr Szopa, "Backward uniqueness of solutions of micropolar fluid equations." Short abstract: Micropolar fluid model is a generalisation of a well-established Navier-Stokes model in the sense that it takes into account the microstructure of a fluid. Several experiments show that it better represents a number of real fluid e.g. blood, especially when the diameter of a domain of flow become small e.g. veins, cappilaries. In general it is not possible to use the solutions of a PDE to define the solution operator S(t) such that u(t)=S(t)u(0) for all t (generally we can do it for positive t). However we show an injectivity or \"backward uniqueness\" property for solutions lying on the attractor A: if S(t)u(0) and S(t)v(0) are two trajectories starting from u(0) and v(0) at t=0 satysfying S(T)u(0)=S(T)v(0) for some T>0 then u(0)=v(0). One can view this property as if there is a solution going backwards in time from u(0) to u(-T), then there can be only one such solution. This implies that (A, S(t)) is a dynamical system. |