Related papers: A Large Data Regime for non-linear Wave Equations
We prove the existence of global solutions to the focusing energy-supercritical semilinear wave equation in R^{3+1} for arbitrary outgoing large initial data, after we modify the equation by projecting the nonlinearity on outgoing states.
In this paper, we give a criterion on the Cauchy data for the semilinear wave equations satisfying the null condition in $\mathbb{R}^+\times\mathbb{R}^{3}$ such that the energy of the data can be arbitrarily large while the solution is…
We generalize the pointwise decay estimates for large data solutions of the defocusing semilinear wave equations which we obtained earlier under restriction to spherical symmetry. Without the symmetry the conformal transformation we use…
We are interested in coupled semi-linear wave equations satisfying the null condition in two space dimensions, a basic model in nonlinear wave equations. Our aim is to establish global existence of smooth solutions to this system with large…
In this paper, we initiate the study of the global stability of nonlinear wave equations with initial data that are not required to be localized around a single point. More precisely, we allow small initial data localized around any finite…
It is well-known that in dimensions at least three semilinear wave equations with null conditions admit global solutions for small initial data. It is also known that in dimension two such result still holds for a certain class of…
We prove global well-posedness of the initial value problem for a class of variational quasilinear wave equations, in one spatial dimension, with initial data that is not-necessarily small. Key to our argument is a form of quasilinear null…
The focusing critical wave equation in three dimensions exhibits a special class of static solutions which are linearly unstable. These solutions decay like an inverse first power. We construct small codimension one stable manifolds in the…
We consider the problem of small data global existence for a class of semilinear wave equations with null condition on a Lorentzian background $(\mathbb{R}^{3+1}, g)$ with a \textbf{time dependent metric $g$} coinciding with Minkowski…
We solve here the so called division problem for wave equations with generic quadratic non-linearities in high dimensions. Specifically, we show that semilinear wave equations which can be written as systems involving quadratic derivative…
We study both of the scattering and Cauchy problems for the semilinear wave equation with null quadratic form on the Schwarzschild background. Prescribing the scattering data that are given by the short pulse data on the future null…
We study the local existence of strong solutions for the cubic nonlinear wave equation with data in $H^s(M)$, $s<1/2$, where $M$ is a three dimensional compact riemannian manifold. This problem is supercritical and can be shown to be…
A key feature of $(1+1)$-dimensional nonlinear wave equations is that they admit left or right traveling waves, under appropriate algebraic conditions on the nonlinearities. In this paper, we prove global stability of such traveling wave…
Fully localised solitary waves are travelling-wave solutions of the three-dimensional gravity-capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence for water of finite depth has recently…
We identify a large class of systems of semilinear wave equations, on fixed accelerated expanding FLRW spacetimes, with nearly at spatial slices, for which we prove small data future global well-posedness. The family of systems we consider…
We establish new bounds of the Sobolev norms of solutions of semilinear wave equations for data lying in the Hs, s<1, closure of compactly supported data inside a ball of radius R, with R a fixed and positive number. In order to do that we…
We prove the existence of global solutions to the nonlinear wave equation in $\mathbb{R}^{1+3}$ $$\Phi_{tt} - \Delta \Phi \pm \Phi|\Phi|^{p-1} = 0$$ in the energy-supercritical regime $p>5$, for a class of large initial data. Our initial…
By introducing new weighted vector fields as multipliers, we derive quantitative pointwise estimates for solutions of defocusing semilinear wave equation in $\mathbb{R}^{1+3}$ with pure power nonlinearity for all $1<p\leq 2$. Consequently,…
The paper is devoted to proving an existence and uniqueness result for generalized solutions to semilinear wave equations with a small nonlinearity in space dimensions 1, 2, 3. The setting is the one of Colombeau algebras of generalized…
In this work we study the global existence for 3d semilinear wave equation with non-negative potential satisfying generic decay assumptions. In the supercritical case we establish the small data global existence result. The approach is…