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We prove that the blow up solutions of type II character constructed by Krieger-Schlag-Tataru [21] as well as Krieger-Schlag [20] are unstable in the energy topology in that there exist open data sets whose closure contains the dataof the preceding type II ...
For the critical focusing wave equation □u=u5 on R3+1 in the radial case, we establish the role of the “center stable” manifold Σ constructed in [18] near the ground state (W,0) as a threshold between blowup and scattering ...
For the critical focusing wave equation □u=u5 on R3+1 in the radial case, we construct a family of blowup solutions which are obtained from the stationary solutions W(r) by means of a dynamical rescaling $\lambda(t)\frac{1}{2}W(\la ...
We study global behavior of radial solutions for the nonlinear wave equation with the focusing energy critical nonlinearity in three and five space dimensions. Assuming that the solution has energy at most slightly more than the ground states and gets away ...
For the radial energy-supercritical nonlinear wave equation □u=−utt+△u=±u7 on R3+1, we prove the existence of a class of global in forward time C∞-smooth solutions with infinite critical Sobolev norm $\dot{H}^{\f ...
We introduce a suitable concept of weak evolution in the context of the radial quintic focussing semilinear wave equation on R^{3+1}, that is adapted to continuation past type II singularities. We show that the weak extension leads to type I singularity fo ...
We consider finite-energy equivariant solutions for the wave map problem from ℝ2+1 to S2 which are close to the soliton family. We prove asymptotic orbital stability for a codimension-two class of initial data which is small with respect to a stronger topo ...
We prove global regularity, scattering and a priori bounds for the energy critical Maxwell-Klein-Gordon equation relative to the Coulomb gauge on (1+4)-dimensional Minkowski space. The proof is based upon a modified Bahouri-Gerard profile decomposition [1] ...
We prove that the critical Wave Maps equation with target S2 and origin R2+1 admits energy class blow up solutions of the form \[ u(t, r) = Q(\lambda(t)r) + \eps(t, r) \] where Q:R2→S2 is the ground state harmonic map and $\lambd ...
In this note we combine a recent result by Geba [2] on the local wellposedness theory of systems of nonlinear wave equations with Q0 null-form structure with the classical Penrose compactification method to obtain a new small data global existence resul ...
