Related papers: Almost global existence for some Hamiltonian PDEs …

In this paper we prove a result of almost global existence for some abstract nonlinear PDEs on flat tori and apply it to some concrete equations, namely a nonlinear Schr\"odinger equation with a convolution potential, a beam equation and a…

We prove an abstract result of almost global existence of small solutions to semi-linear Hamiltonian partial differential equations satisfying very weak non resonance conditions and basic multilinear estimates. Thanks to works by…

This paper is devoted to the proof of almost global existence results for Klein-Gordon equations on Zoll manifolds (e.g. spheres of arbitrary dimension) with Hamiltonian nonlinearities, when the Cauchy data are smooth and small. The proof…

In this paper, we prove almost global existence of solutions to certain quasilinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides with Neumann boundary conditions. We use a Galerkin method to expand the…

The aim of this article is to prove an "almost" global existence result for some semilinear wave equations in the plane outside a bounded convex obstacle with the Neumann boundary condition.

We describe some recent results on existence of quasi-periodic solutions of Hamiltonian PDEs on compact manifolds. We prove a linear stability result for the non-linear Schr\"odinger equation in the case of $SU(2)$ and $SO(3)$.

In this article we prove that stochastic differential equation (SDE) with Sobolev drift on compact Riemannian manifold admits a unique $\nu$-almost everywhere stochastic invertible flow, where $\nu$ is the Riemannian measure, which is…

We prove almost global existence for semilinear wave equations outside of nontrapping obstacles. We use the vector field method, but only use the generators of translations and Euclidean rotations. Our method exploits 1/r decay of wave…

For any subcritical index of regularity $s>3/2$, we prove the almost global well posedness for the 2-dimensional semilinear wave equation with the cubic nonlinearity in the derivatives, when the initial data are small in the Sobolev space…

We present a general existence proof for a wide class of non-linear elliptic equations which can be applied to problems with barrier conditions without specifying any assumptions guaranteeing the uniqueness or local uniqueness of particular…

The only one example has been known of magnetic geodesic flow on the 2-torus which has a polynomial in momenta integral independent of the Hamiltonian. In this example the integral is linear in momenta and corresponds to a one parametric…

We prove almost global existence for supercritical nonlinear Schr\"odinger equations on the $d$-torus ($d$ arbitrary) on the good geometry selected in part I. This is seen as the Cauchy consequence of I, since the known invariant measure of…

We show a global existence result for a doubly nonlinear porous medium type equation of the form $$u_t = \Delta_p u^m +\, u^q$$ on a complete and non-compact Riemannian manifold $M$ of infinite volume. Here, for $1<p<N$, we assume…

In our previous paper [Fei Hou, Fei Tao, Huicheng Yin, Global existence and scattering of small data smooth solutions to a class of quasilinear wave systems on $\mathbb{R}^2\times\mathbb{T}$, Preprint (2024), arXiv:2405.03242], for the…

We study the global existence of solutions to semilinear wave equations with power-type nonlinearity and general lower order terms on $n$ dimensional nontrapping asymptotically Euclidean manifolds, when $n=3, 4$. In addition, we prove…

In this paper we consider rough differential equations on a smooth manifold $\left( M\right) .$ The main result of this paper gives sufficient conditions on the driving vector-fields so that the rough ODE's have global (in time) solutions.…

We prove that under certain stability and smoothing properties of the semi-groups generated by the partial differential equations that we consider, manifolds left invariant by these flows persist under $C^1$ perturbation. In particular, we…

We prove that wave maps that factor as $\mathbb{R}^{1+d} \overset{\varphi_{\text{S}}}{\to} \mathbb{R} \overset{\varphi_{\text{I}}}{\to} M$, subject to a sign condition, are globally nonlinear stable under small compactly supported…

In this paper we prove global and almost global existence theorems for nonlinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides. We can handle both the case of Dirichlet boundary conditions and Neumann…

We prove the global existence of the small solutions to the Cauchy problem for quasilinear wave equations satisfying the null condition on $(R^3, g)$, where the metric $g$ is a small perturbation of the flat metric and approaches the…