Related papers: Norm inflation for generalized magneto-hydrodynami…
We demonstrate that the solutions to the Cauchy problem for the three dimensional incompressible magneto-hydrodynamics (MHD) system can develop diferent types of norm inflations in $\dot{B}_{\infty}^{-1, \infty}$. Particularly the magnetic…
We demonstrate that the solutions to the Cauchy problem for the three dimensional incompressible magneto-hydrodynamics (MHD) system can develop diferent types of norm inflations in $\dot{B}_{\infty}^{-1, \infty}$. Particularly the magnetic…
We consider the incompressible Navier-Stokes equation with a fractional power $\alpha\in[1,\infty)$ of the Laplacian in the three dimensional case. We prove the existence of a smooth solution with arbitrarily small in…
We consider the ideally conducting, viscous magnetohydrodynamics (MHD) equations in two dimensions. Specifically, we study the nonlinear dynamics near a combination of Couette flow and a constant magnetic field in a periodic infinite…
We demonstrate that the three dimensional incompressible magneto-hydrodynamics (MHD) system is ill-posed due to the discontinuity of weak solutions in a wide range of spaces. Specifically, we construct initial data which has finite energy…
We prove that the incompressible Navier-Stokes equations exhibit norm inflation in $\dot B^{s}_{p,q}(\mathbb{R}^3)$ with smooth, compactly supported initial data. Such norm inflation is shown in all supercritical $\dot B^{s}_{p,q} $ near…
In the standard cosmological picture the Universe underwent a brief period of near-exponential expansion, known as Inflation. This provides an explanation for structure formation through the amplification of perturbations by the rapid…
We prove the ill-posedness for the 3D incompressible inhomogeneous Navier-stokes equations in critical Besov space. In particular, a norm inflation happens in finite time with the initial data satisfying…
We consider D-term hybrid inflation in the framework of superconformal supergravity. In part of the parameter space, inflation continues for subcritical inflaton field value. Consequently, a new type of inflation emerges, which gives…
Inflation is well known to be difficult in the context of supergravity, if the potential is dominated by the $F$ term. Non-renormalizable terms generically give $|V''|\sim V/M^2$, where $V(\phi)$ is the inflaton potential and $M$ is the…
Using only general properties of the tachyon potential we show that inflation may be generic when many branes and anti-branes become coincident. Inflation may occur because of: (1) the assistance of the many diagonal tachyon fields; (2)…
The pre-big bang's inflationary mechanism, when allowance is made for the rapid change of Newton's constant, is not actually of pole-law form . We give examples where pole-law inflation, which requires violation of the weak-energy…
We demonstrate that the three dimensional incompressible magneto-hydrodynamics (MHD) system is ill-posed in the largest scaling invariant space $\dot{B}_{\infty,\infty}^{-1}$. The construction method of initial data used in this paper is…
We prove the norm inflation phenomena for the Boussinesq system on $\mathbb T^3$. For arbitrarily small initial data $(u_0,\rho_0)$ in the negative-order Besov spaces $\dot{B}^{-1}_{\infty, \infty} \times \dot{B}^{-1}_{\infty, \infty}$, the…
A model of cosmological inflation is proposed in which field space is a hyperbolic plane. The inflaton never slow-rolls, and instead orbits the bottom of the potential, buoyed by a centrifugal force. Though initial velocities redshift away…
It is well known that the three-dimensional ideal magnetohydrodynamics (MHD) equations possess three magnetic invariants: (M) magnetic helicity, (C) cross helicity, and (P) the mean-square magnetic potential, in addition to the fundamental…
In this paper, we establish the global existence to the three-dimensional incompressible Hall-MHD equations for a class of large initial data, whose $L^{\infty}$ norms can be arbitrarily large.
Higgs inflation can occur if the Standard Model (SM) is a self-consistent effective field theory up to inflationary scale. This leads to a lower bound on the Higgs boson mass, $M_h \geq M_{\text{crit}}$. If $M_h$ is more than a few hundreds…
We consider a scale-invariant helical magnetic field generated during inflation. We show that, if the mean magnetic helicity density of such a field is measured, it can be used to determine a lower bound on the duration of inflation. Upper…
Inflation may have been driven by a component which violated the Null-Energy Condition, thereby leading to {\it super inflation}. We provide the formalism to study cosmological perturbations when such a component is described by a scalar…