Yuri Cacchiò

Long time strong Sobolev instability for quasilinear NLS

We prove long-time strong Sobolev instability for a class of quasilinear Schr\"odinger equations on $\mathbb T^2$ arising, via the Madelung transform, in the description of Euler-Korteweg capillary fluids. More precisely, for every $s\ge 7$, arbitrarily small $\mu>0$, and arbitrarily large $\mathcal K>0$, we construct...