I know little about these issues, so my questions may be dumb. 1. Do exact solutions exist for non-Abelian gauge theory without matter fields? 2. Do exact solutions exist for Abelian/Non-Abelian theory with matter fields (scalar or spinor)? 2. Are solutions well-behaved? I'm asking because no one can prove it for Navier-Stokes equation. Another reason is that Non-linear waves can develop singularities, and gluons fields are non-linear waves.