Related papers: Large Initial Data Global Well-Posedness for a Sup…

In this paper we show that after suitable data randomization there exists a large set of super-critical periodic initial data, in $H^{-\alpha}({\mathbb T}^d)$ for some $\alpha(d) > 0$, for both 2d and 3d Navier-Stokes equations for which…

In this paper, we study the characteristic initial value problem for a class of nonlinear wave equations with data on a conic light cone in the Minkowski space $\mathbb{R}^{1+3}$. We show the existence of local solution for a class of…

In this paper we study the existence of global-in-time energy solutions to the Cauchy problem for the Euler-Poisson-Darboux equation, with a power nonlinearity: $$u_{tt}-u_{xx} + \frac\mu{t}\,u_t = |u|^p \,, \quad t>t_0, \…

We establish existence and uniqueness of global, bounded weak solutions to quasilinear PDEs with bounded, uniformly continuous initial data and investigate their properties. Moreover, we establish existence of bounded weak solutions when…

In this paper, we study the semilinear wave equations with the inverse-square potential. By transferring the original equation to a "fractional dimensional" wave equation and analyzing the properties of its fundamental solution, we…

In this paper, a strongly damped semilinear wave equation with a general nonlinearity is considered. With the help of a newly constructed auxiliary functional and the concavity argument, a general finite time blow-up criterion is…

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…

In this work, we consider the 3D defocusing energy-critical nonlinear Schr\"odinger equation $i\partial_t u+\Delta u =|u|^4 u,\quad (t,x)\in \mathbb{R}\times \mathbb{R}^3$. Applying the outgoing and incoming decomposition presented in the…

In this paper, we prove the global well-posedness for the 3D rotating Navier-Stokes equations in the critical functional framework. Especially, this result allows to construct global solutions for a class of highly oscillating initial data.

We prove global pointwise decay estimates for a class of defocusing semilinear wave equations in $n=3$ dimensions restricted to spherical symmetry. The technique is based on a conformal transformation and a suitable choice of the mapping…

In this paper we show existence of finite energy solutions for the Cauchy problem associated with a semilinear wave equation with interior damping and supercritical source terms. The main contribution consists in dealing with…

We prove global well-posedness for low regularity data for the one dimensional quintic defocusing nonlinear Schr\"odinger equation. Precisely we show that a unique and global solution exists for initial data in the Sobolev space…

This paper is concerned with a quaslinear parabolic equation including a nonlinear nonlocal initial condition. The problem arises as equilibrium equation in population dynamics with nonlinear diffusion. We make use of global bifurcation…

This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results for some semilinear nonlocal wave equations. The main…

We show existence of global strong solutions with large initial data on the irrotational part for the shallow-water system in dimension $N\geq 2$. We introduce a new notion of \textit{quasi-solutions} when the initial velocity is assumed to…

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…

This paper deals with a class of semilinear wave equation with nonlinear damping term $|u_{t}|^{m-2}u_t $ and nonlinear source term $g(x)|u|^{p-2}u$ on the manifolds with conical singularities. Firstly, we prove the local existence and…

The study of Einstein equations leads naturally to Cauchy problems with initial data on hypersurfaces which closely resemble hyperboloids in Minkowski space-time, and with initial data with polyhomogeneous asymptotics, that is, with…

We prove that solution of defocusing semilinear wave equation in $\mathbb{R}^{1+3}$ with pure power nonlinearity is uniformly bounded for all $\frac{3}{2}<p\leq 2$ with sufficiently smooth and localized data. The result relies on the…

We show global existence backwards from scattering data at infinity for semilinear wave equations satisfying the null condition or the weak null condition. Semilinear terms satisfying the weak null condition appear in many equations in…