Loading...
research article
Optimal polynomial blow up range for critical wave maps
We prove that the critical Wave Maps equation with target $S^2$ and origin $\R^{2+1}$ admits energy class blow up solutions of the form $[ u(t, r) = Q(\lambda(t)r) + \eps(t, r) ]$ where $Q:\R^2\rightarrow S^2$ is the ground state harmonic map and $\lambda(t) = t^{-1-\nu}$ for any $\nu>0$. This extends the work $\cite{KST0}$, where such solutions were constructed under the assumption $\nu>\frac{1}{2}$. In light of a result of Struwe $\cite{Struwe1}$, our result is optimal for polynomial blow up rates.
Loading...
Name
CanWM1.pdf
Access type
openaccess
Size
478.42 KB
Format
Adobe PDF
Checksum (MD5)
b14f540ac1198b6ae22f604aeea8fee6