# Quintic NLW/NLKG on R

• Scaling is ${\displaystyle s_{c}=0}$.
• LWP for ${\displaystyle s\geq 3/10}$ by energy estimates and Sobolev (solution is in ${\displaystyle L_{x}^{5}}$)
• For ${\displaystyle s<3/10}$ one has ill-posedness CtCoTa-p2, indeed it is not even possible to make sense of solutions in the distributional sense.
• GWP for ${\displaystyle s\geq 1}$ in the defocussing case from energy conservation.
• It is overwhelmingly likely that one can lower this s index.
• In the focussing case there is blowup from large data by the ODE method.