# Septic NLW/NLKG on R

• Scaling is ${\displaystyle s_{c}=1/6}$.
• LWP for ${\displaystyle s\geq 5/14}$ by energy estimates and Sobolev (solution is in ${\displaystyle L_{x}^{7}}$)
• For ${\displaystyle s<5/14}$ it is not even possible to make sense of the solution as a distribution (note there are no smoothing effects for the 1D wave equation!) and so there is ill-posedness CtCoTa-p2.
• GWP for ${\displaystyle s=1}$ in the defocusing case by energy conservation. Presumably this is improvable.