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We consider the FENE dumbbell polymer model which is the coupling of theincompressible Navier-Stokes equations with the correspondingFokker-Planck-Smoluchowski di ffusion equation. We show global well-posednessin the case of a 2D bounded domain. We assume in the general case that theinitial velocity is sufficiently small and the initial probability density issufficiently close to the equilibrium solution; moreover an additionalcondition on the coeffcients is imposed. In the corotational case, we onlyassume that the initial probability density is sufficiently close to theequilibrium solution.

The FENE dumbbell polymer model: existence and uniqueness of solutions for the momentum balance equation