Fourier spectral approximation to a dissipative system modeling the flow of liquid crystals

We study a Fourier-spectral method for a dissipative system modeling the ow of liquid crystals. We rst prove its convergence in a suitable sense and e stablish the existence of a global weak solution of the original problem an d its uniqueness in the two dimensional case. Then we derive error estimate s which exhibit the spectral accuracy of the Fourier-spectral method. We al so construct a fully discrete scheme and carry out a complete stability and error analysis for it. Finally, we present some illustrative numerical res ults.