# Existence and smoothness for viscous Burgers equation?

What do we currently know about (references please!) the existence and smoothness of solutions to the viscous Burgers equation, in 1D, 2D, and 3D?

• I think it would be appropriate to capitalize "Burgers". Viscous burgers sound really yucky. – Andreas Blass Mar 10 '19 at 22:17

It is shown that the homogeneous viscous Burgers equation in $$d$$ spatial dimensions has a globally defined smooth solution if the initial condition is a smooth function growing like $$o(|x|)$$ at infinity.