Global well-posedness for volume–surface reaction–diffusion systems

Global Well-posedness of Nls-kdv Systems for Periodic Functions

We prove that the Cauchy problem of the Schrödinger-KortewegdeVries (NLS-KdV) system for periodic functions is globally well-posed for initial data in the energy space H1×H1. More precisely, we show that the nonresonant NLS-KdV system is globally well-posed for initial data in Hs(T) × Hs(T) with s > 11/13 and the resonant NLS-KdV system is globally wellposed with s > 8/9. The strategy is to app...

Well-posedness of Hybrid Systems

Sharp Global Well - Posedness for Kdv and Modified Kdv On

The initial value problems for the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations under periodic and decaying boundary conditions are considered. These initial value problems are shown to be globally well-posed in all L 2-based Sobolev spaces H s where local well-posedness is presently known, apart from the H 1 4 (R) endpoint for mKdV. The result for KdV relies on a new method for co...

Probabilistic global well-posedness for the supercritical nonlinear harmonic oscillator

— Thanks to an approach inspired from Burq-Lebeau [6], we prove stochastic versions of Strichartz estimates for Schrödinger with harmonic potential. As a consequence, we show that the nonlinear Schrödinger equation with quadratic potential and any polynomial nonlinearity is almost surely locally well-posed in L(R) for any d ≥ 2. Then, we show that we can combine this result with the high-low fr...

Global Well-posedness for Cubic Nls with Nonlinear Damping

u(0) = u0(x), with given parameters λ ∈ R and σ > 0, the latter describing the strength of the dissipation within our model. We shall consider the physically relevant situation of d 6 3 spatial dimensions and assume that the dissipative nonlinearity is at least of the same order as the cubic one, i.e. p > 3. However, in dimension d = 3, we shall restrict ourselves to 3 6 p 6 5. In other words, ...