Sharp well-posedness results for the generalized Benjamin-Ono equation with high nonlinearity

We establish the local well-posedness of the generalized Benjamin-Ono equation $\partial_tu+\mathcal{H}\partial_x^2u\pm u^k\partial_xu=0$ in $H^s(\R)$, $s>1/2-1/k$ for $k\geq 12$ and without smallness assumption on the initial data. The condition $s>1/2-1/k$ is known to be sharp since the solution map $u_0\mapsto u$ is not of class $\mathcal{C}^{k+1}$ on $H^s(\R)$ for $s<1/2-1/k$. On the other hand, in the particular case of the cubic Benjamin-Ono equation, we prove the ill-posedness in $H^s(\R)$, $s<1/3$

Glueball-Meson Mixing

Calculations in unquenched QCD for the scalar glueball spectrum have confirmed previous results of Gluodynamics finding a glueball at ~ 1750 MeV. I analyze the implications of this discovery from the point of view of glueball-meson mixing at the light of the experimental scalar sprectrum.Comment: 7 pages, 5 figure

AdS gravity and glueball spectrum

The glueball spectrum has attracted much attention since the formulation of Quantum Chromodynamics. Different approaches give very different results for their masses. We revisit the problem from the perspective of the AdS/CFT correspondence.Comment: 4 pages, no figures, 5 table