Blow-up solutions of the "bad" Boussinesq equation
Blow-up solutions of the "bad" Boussinesq equation
We study blow-up solutions of the ``bad" Boussinesq equation, and prove that a wide range of asymptotic scenarios can happen. For example, for each $T>0$, $x_{0}\in \mathbb{R}$ and $\delta \in (0,1)$, we prove that there exist Schwartz class solutions $u(x,t)$ on $\mathbb{R} \times [0,T)$ such that $|u(x,t)| \leq C \frac{1+x^{2}}{(x-x_{0})^{2}}$ …