相关论文: Soliton resolution for critical co-rotational wave…
In this paper, we prove the soliton resolution conjecture for general type II solutions to the focusing energy critical wave equation, in space dimension 3,4 or 5, along a sequence of times. This is an important step towards the full…
In this paper, we establish the soliton resolution for the energy critical wave equation with inverse square potential in the radial case and in all dimensions $N\geq3$. The structure of the radial linear operator $\mathcal{L}_a :=-\Delta…
We establish the Soliton Resolution Conjecture for the radial critical non-linear heat equation in dimension $D\geq 3.$ Thus, every finite energy solution resolves, continuously in time, into a finite superposition of asymptotically…
We consider the equivariant wave maps equation $\mathbb{R}^{1+2} \to \mathbb{S}^2$, in all equivariance classes $k \in \mathbb{N}$. We prove that every finite energy solution resolves, continuously in time, into a superposition of…
We consider the focusing energy-critical nonlinear wave equation for radially symmetric initial data in space dimensions $D \ge 4$. This equation has a unique (up to sign and scale) nontrivial, finite energy stationary solution $W$, called…
In this article we discuss the long-time dynamics of the radial solutions to the energy-critical wave equation in 3-dimensional space. Given a solution defined for all time $t\geq 0$, we show that the soliton resolution phenomenon happens…
We show that any finite energy solution of the energy-critical nonlinear heat flow in dimensions $d\geq 3$ asymptotically resolves into a sum of possibly time-dependent solitons, a radiation term, and an error term that vanishes in the…
In this paper we give a unified proof to the soliton resolution conjecture along a sequence of times, for the semilinear focusing energy critical wave equations in the radial case and two dimensional equivariant wave map equations,…
Consider the energy-critical focusing wave equation in odd space dimension $N\geq 3$. The equation has a nonzero radial stationary solution $W$, which is unique up to scaling and sign change. In this paper we prove that any radial, bounded…
In this article we discuss the long-time dynamics of the radial solutions to the focusing energy-critical wave equation in 5-dimensional space. We give some details about the asymptotic behaviour, topological structure and time evolution of…
In this paper, we study the soliton resolution conjecture for Type II singular solutions $\overrightarrow{u}(t)$ to the focusing energy critical wave equation in $R^d\times [0,T_+)$, with $3\leq d\leq 5$. Suppose that $u$ has a singularity…
We consider the energy-critical wave maps equation from 1+2 dimensional Minkowski space into the 2-sphere, in the equivariant case. We prove that if a wave map decomposes, along a sequence of times, into a superposition of at most two…
Consider the energy-critical focusing wave equation in space dimension $N\geq 3$. The equation has a nonzero radial stationary solution $W$, which is unique up to scaling and sign change. It is conjectured (soliton resolution) that any…
We consider the quadratic semilinear wave equation in six dimensions. This energy critical problem admits a ground state solution, which is the unique (up to scaling) positive stationary solution. We prove that any spherically symmetric…
We consider finite energy corotationnal wave maps with target manifold $\m S^2$. We prove that for a sequence of times, they decompose as a sum of decoupled harmonic maps in the light cone, and a smooth wave map (in the blow case) or a…
In this paper, we continue our study of equivariant \emph{wave maps on a wormhole} initiated in our companion paper. More precisely, we study finite energy $\ell$--equivariant wave maps from the (1+3)-dimensional spacetime $\mathbb R \times…
We study the energy-critical half-wave maps equation: \[ \partial_t \mathbf{u} = \mathbf{u} \times |D| \mathbf{u} \] for $\mathbf{u} : [0, T) \times \mathbb{R} \to \mathbb{S}^2$. Our main result establishes the global existence and…
This work concerns a general system of energy-critical wave equations in the Minkowski space of dimension $1+3$. The wave equations are coupled by the nonlinearities, which are homogeneous of degree 5. We prove that any radial solution of…
We consider energy-critical damped wave equation \begin{equation*} \partial_{tt}u-\Delta u+\alpha \partial_t u=\left|u\right|^{\frac{4}{D-2}}u \end{equation*} with radial initial data in dimensions $D\geq 4$. The equation has a nontrivial…
We prove exterior energy lower bounds for (nonradial) solutions to the energy-critical nonlinear wave equation in space dimensions $3 \le d \le 5$, with compactly supported initial data. In particular, it is shown that nontrivial global…