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We continue the study of low regularity behavior of the viscous nonlinear wave equation (vNLW) on $mathbb R^2$, initiated by v{C}anic and the first author (2021). In this paper, we focus on the defocusing quintic nonlinearity and, by combining a parabolic smoothing with a probabilistic energy estimate, we prove almost sure global well-posedness of vNLW for initial data in $mathcal H^s (mathbb R^2)$, $s >- frac 15$, under a suitable randomization.
We prove global well-posedness for 3D Dirac equation with a concentrated nonlinearity.
We prove global well-posedness for the 3D Klein-Gordon equation with a concentrated nonlinearity.
In this paper we prove local well-posedness in Orlicz spaces for the biharmonic heat equation $partial_{t} u+ Delta^2 u=f(u),;t>0,;xinR^N,$ with $f(u)sim mbox{e}^{u^2}$ for large $u.$ Under smallness condition on the initial data and for exponential
We prove global well-posedness for the $3D$ radial defocusing cubic wave equation with data in $H^{s} times H^{s-1}$, $1>s>{7/10}$.
We establish probabilistic small data global well-posedness of the energy-critical Maxwell-Klein-Gordon equation relative to the Coulomb gauge for scaling super-critical random initial data. The proof relies on an induction on frequency procedure and