We investigate the stability and stabilization of the cubic focusing Klein–Gordon equation around static solutions on the closed ball of radius L in R3. First we show that the system is linearly unstable near the static solution u ≡ 1 for any dissipative b ...
We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation [ \Box u = -u^5 ] on R3+1 constructed in \cite{KST}, \cite{KS1} are stable along a co-dimension one Lipschitz manifold of data perturbations in a ...
We prove the semi-global controllability and stabilization of the (1+1)−dimensional wave maps equation with spatial domain 𝕊1 and target Sk. First we show that damping stabilizes the system when the energy is strictly below the threshold 2π, where ha ...
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 a mod ...
We exhibit non-equivariant perturbations of the blowup solutions constructed in [18] for energy critical wave maps into S2. Our admissible class of perturbations is an open set in some sufficiently smooth topology and vanishes near the light co ...
We introduce a novel data randomisation for the free wave equation which leads to the same range of Strichartz estimates as for radial data, albeit in a non-radial context. We then use these estimates to establish global wellposedness for a wave maps type ...
We prove that the half-wave maps problem on R4+1 with target S2 is globally well-posed for smooth initial data which are small in the critical l1 based Besov space. This is a formal analogue of the result [17]. ...
We show that the finite time blow up solutions for the co-rotational Wave Maps problem constructed in [7,15] are stable under suitably small perturbations within the co-rotational class, provided the scaling parameter λ(t)=t−1−ν is sufficiently close to ...
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 a mod ...
Continuing the investigations started in the recent work [12] on semi-global controllability and stabilization of the (1+1)-dimensional wave maps equation with spatial domain S1 and target Sk , where semi-global refers to the 2π-energy bound, we prov ...
