9 problems

The wave-turbulence model yields a curve of steady solutions for the oceanic internal-wave energy spectrum, and individual observations lie at different positions along this curve.…

Nonlinear saturation conjecture. The resulting phase coherence will lead to a nonlinear amplitude saturation which will stop the wave predicted by the theory, and this will in turn…

Let $W_k=W_k(t,x)$ denote the energy spectrum, let $\bm{k}=(k_1,k_2,k_3)\in\mathbb{R}^{3d}$, and define … Let $\Omega(\bm{k})$ be the resonance factor defined in the source, and le…

Let the self-similar solution of the wave kinetic equation have frequency variable $omega$ and let $x^*$ denote the exponent determined by the associated nonlinear eigenvalue probl…

Kinetic wave equation conjecture. There exists a kinetic time scale, depending on the frequency localisation of the data and on the strength of the nonlinearity, on which the expec…

Wave kinetic equation conjecture. As $L\to\infty$, $t\to\infty$, and $\lambda^2/L^d\to0$, one has

Wave turbulence conjecture. As $L\to\infty$ and $\lambda^2/L^d\to0$, the quantity $\rho_k^L(t)$ converges to a solution of a kinetic equation.

Six-wave kinetic-equation conjecture. By analogy with the four-wave kinetic equation, the six-wave kinetic equation should have the form

Quasi-equilibrium conjecture. Quasisolitons and quasibreathers exist only in quasi-equilibrium with a weakly nonlinear wave-noise environment.