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

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  • $\begingroup$ I think it would be appropriate to capitalize "Burgers". Viscous burgers sound really yucky. $\endgroup$
    – Andreas Blass
    Commented Mar 10, 2019 at 22:17

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Global existence and smoothness for solutions of viscous Burgers equation (2015).

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.

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