相关论文: A remark on norm inflation for nonlinear wave equa…

We study the two-dimensional periodic nonlinear Schr\"odinger equation (NLS) with the quadratic nonlinearity $|u|^2$. In particular, we study the quadratic NLS with random initial data distributed according to a fractional derivative (of…

We study the Cauchy problem for the cubic fractional nonlinear Schr\"odinger equation (fNLS) on the real line and on the circle. In particular, we prove global well-posedness of the cubic fNLS with all orders of dispersion higher than the…

We investigate the impact of Coleman-Weinberg inflation on the stochastic gravity wave background spectrum emitted by intermediate scale cosmic strings. The string network is partially inflated and re-enters the horizon at later times after…

In this paper, we study the Cauchy problem of the 3-dimensional (3D) generalized incompressible Navier-Stokes equations (gNS) in Triebel-Lizorkin space $\dot{F}^{-\alpha,r}_{q_\alpha}(\mathbb{R}^3)$ with…

Systems of wave equations may fail to be globally well posed, even for small initial data. Attempts to classify systems into well and ill-posed categories work by identifying structural properties of the equations that can work as…

We investigate the possibility that nonlinear gravitational effects influence the preheating era after inflation. Our work is based on numerical solutions of the inhomogeneous Einstein field equations, and is free of perturbative…

Cosmic inflation is arguably the most favoured paradigm of the very early Universe. It postulates an early phase of fast, nearly exponential, and accelerated expansion. Inflationary models are capable of explaining the overall flatness and…

We consider the Cauchy problem for the defocusing energy-critical stochastic nonlinear wave equations (SNLW) with an additive stochastic forcing on $\mathbb{R}^{d}$ and $\mathbb{T}^{d}$ with $d \geq 3$. By adapting the probabilistic…

We investigate how inflation model selection is affected by the presence of additional free-streaming relativistic degrees of freedom, i.e. dark radiation. We perform a full Bayesian analysis of both inflation parameters and cosmological…

We consider the linear wave equation $V(x) u_{tt}(x, t) - u_{xx}(x, t) = 0$ on $[0, \infty)\times[0, \infty)$ with initial conditions and a nonlinear Neumann boundary condition $u_x(0, t) = (f(u_t(0,t)))_t$ at $x=0$. This problem is an…

Inflationary paradigm has several issues, such as the pre-inflationary horizon problem or the eternal inflation. To avoid that the standard Starobinsky inflation has been extended to $R + \alpha R^n$ and $R + \alpha R^n -\delta R^{2-n}$…

We present a technique, {\em the uniform asymptotic approximation}, to construct accurate analytical solutions of the linear perturbations of inflation after quantum effects of the early universe are taken into account, for which the…

We study regularization of ill-posed equations involving multiplication operators when the multiplier function is positive almost everywhere and zero is an accumulation point of the range of this function. Such equations naturally arise…

Power-law inflation has stood as a classical model in inflationary cosmology since the early 1980s, prized for its exact analytical solutions and ability to naturally resolve the Big Bang theory's horizon and flatness problems through…

We consider the eternal inflation scenario of the slow-roll/chaotic type with the additional element of an objective collapse of the wave function. The incorporation of this new agent to the traditional inflationary setting might represent…

This article investigates the well-posedness of weak solutions to non-linear parabolic PDEs driven by rough coefficients with rough initial data in critical homogeneous Besov spaces. Well-posedness is understood in the sense of existence…

It is well known that large Hubble-induced supergravity corrections to the inflaton field can ruin the flatness of the potential, thus creating a tension between slow-roll inflation and supergravity. In this paper we show that it is…

In the early Universe matter can be described as a conformal invariant ultra-relativistic perfect fluid, which does not contribute, on classical level, to the evolution of the isotropic and homogeneous metric. If we suppose that there is…

We show that expanding or contracting Kasner universes are unstable due to the amplification of gravitational waves (GW). As an application of this general relativity effect, we consider a pre-inflationary anisotropic geometry characterized…

The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions,…