Elliptic Equations In Fluid Mechanics

This work tries to state some interesting results about the elliptic equations oc-curing in solving the systems in fluid mechanics in the whole space, such as the C(?) estimates, the L2 estimates and the Lp estimates. We mainly use the Fourier analysis to deal with the Holder solution space, the Lax-Milgram theorem to solve the L2 case and Calderon-Zygmund theory to the Lp space. The results are sometimes different from the classical results in bounded domain, due to the singularity at infinity.