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Register a new userBlowup stability at optimal regularity for the critical wave equation
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We establish Strichartz estimates for the radial energy-critical wave equation in 5 dimensions in similarity coordinates. Using these, we prove the nonlinear asymptotic stability of the ODE blowup in the energy space.
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We establish Strichartz estimates in similarity coordinates for the radial wave equation in three spatial dimensions with a (time-dependent) self-similar potential. As an application we consider the critical wave equation and prove the asymptotic stability of the ODE blowup profile in the energy space.
We consider the wave equation with a focusing cubic nonlinearity in higher odd space dimensions without symmetry restrictions on the data. We prove that there exists an open set of initial data such that the corresponding solution exists in a backward light-cone and approaches the ODE blowup profile.
We study the blowup behavior for the focusing energy-supercritical semilinear wave equation in 3 space dimensions without symmetry assumptions on the data. We prove the stability of the ODE blowup profile.
We study the blowup behavior of a class of strongly perturbed wave equations with a focusing supercritical power nonlinearity in three spatial dimensions. We show that the ODE blowup profile of the unperturbed equation still describes the asymptotics of stable blowup. As a consequence, stable ODE-type blowup is seen to be a universal phenomenon that exists in a large class of semilinear wave equations.
We consider wave maps on $(1+d)$-dimensional Minkowski space. For each dimension $dgeq 8$ we construct a negatively curved, $d$-dimensional target manifold that allows for the existence of a self-similar wave map which provides a stable blowup mechanism for the corresponding Cauchy problem.
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