相关论文: Adapted Linear-Nonlinear Decomposition And Global …
We prove global well-posedness for the $3D$ radial defocusing cubic wave equation with data in $H^{s} \times H^{s-1}$, $1>s>{7/10}$.
In this paper, we prove global well-posedness and scattering for the defocusing, cubic nonlinear Schr{\"o}dinger equation in three dimensions when $n = 3$ when $u_{0} \in H^{s}(\mathbf{R}^{3})$, $s > 3/4$. To this end, we utilize a…
In this paper we prove global well-posedness and scattering for the defocusing, cubic, nonlinear wave equation on $\mathbf{R}^{1 + 3}$ with radial initial data lying in the critical Sobolev space $\dot{H}^{1/2}(\mathbf{R}^{3}) \times…
We prove global well-posedness and scattering for the defocusing, cubic NLS on $\mathbb{R}^3$ with initial data in $H^s(\mathbb{R}^3)$ for $s>49/74$. The proof combines the ideas of resonance decomposition in \cite{CKSTT4} and…
In this paper we prove a global well-posedness and scattering result for the defocusing conformal nonlinear wave equation in the hyperbolic space $\mathbb{H}^d, d \geq 3$. We take advantage of the hyperbolic geometry which yields stronger…
The paper deals with the defocusing case of the energy subcritical non-linear wave equation in $R^3$. We assume the initial data is in the space $\dot{H}^s \times \dot{H}^{s-1}$ and radial. If $s=1$, this is the energy space and the…
In this paper we study the defocusing, cubic nonlinear wave equation in three dimensions with radial initial data. The critical space is $\dot{H}^{1/2} \times \dot{H}^{-1/2}$. We show that if the initial data is radial and lies in…
In this paper we prove that the cubic wave equation is globally well - posed and scattering for radial initial data lying in $B_{1,1}^{2} \times B_{1,1}^{1}$. This space of functions is a scale invariant subspace of $\dot{H}^{1/2} \times…
We prove almost sure global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on $\mathbb{R}^3$ with random initial data in $ H^s(\mathbb{R}^3) \times H^{s-1}(\mathbb{R}^3)$ for $s > \frac 12$. The main new…
In this article, we investigate the global well-posedness for the defocusing, cubic nonlinear Schr\"{o}dinger equation posed on $\T^3$ with intial data lying in its critical space $H^\frac{1}{2}(\T^3)$. By establishing the linear profile…
In this paper, we prove the global well-posedness of defocusing 3D quadratic nonlinear Schr\"odinger equation \begin{align*} i\partial_t u + \frac12\Delta u = |u| u, \end{align*} in its sharp critical weighted space $\mathcal F \dot…
This article is devoted to a general class of one dimensional NLS problems with a cubic nonlinearity. The question of obtaining scattering, global in time solutions for such problems has attracted a lot of attention in recent years, and…
In this paper, we study the theory of the global well-posedness and scattering for the energy-critical wave equation with a cubic convolution nonlinearity $u_{tt}-\Delta u+(|x|^{-4}\ast|u|^2)u=0$ in spatial dimension $d \geq 5$. The main…
In this paper, we study the global well-posedness and scattering of 3D defocusing, cubic Schr\"odinger equation. Recently, Dodson [arXiv:2004.09618] studied the global well-posedness in a critical Sobolev space $\dot{W}^{11/7,7/6}$. In this…
In this article, we show that the solution to defocusing cubic nonlinear Schr\"odinger equation (NLS) posed on the two-dimensional waveguide \begin{align*} i\partial_tu+\Delta_{\R\times\T}u=|u|^2u \end{align*} is globally well-posed in…
The three dimensional cubic defocusing nonlinear wave equation is known to be ill-posed for general low regularity initial data. However, well-posedness can be recovered globally in time on a probabilistic level when considering random…
In this paper we prove that the cubic wave equation is globally well - posed and scattering for radial initial data lying in a slightly supercritical Sobolev space, and a weighted Sobolev space.
We study the long time behavior of the subcritical (subcubic) defocussing nonlinear wave equation on the three dimensional ball, for random data of low regularity. We prove that for a large set of radial initial data in $\cap_{s<1/2}…
We study the critical dissipative quasi-geostrophic equations in $\bR^2$ with arbitrary $H^1$ initial data. After showing certain decay estimate, a global well-posedness result is proved by adapting the method in [11] with a suitable…
In this article, we follow the strategies, listed in \cite{Burq2011} and \cite{OhPo}, in dealing with supercritical cubic and quintic wave equations, we obtain that, the equation \begin{equation*} \left\{ \begin{split}…