11 citations · 23 across the 5 of their papers we have counts for
5 papers
Symplectic Normal Form and Growth of Sobolev Norm
Zhenguo Liang, Jiawen Luo, Zhiyan Zhao
For a class of reducible Hamiltonian partial differential equations (PDEs) with arbitrary spatial dimensions, quantified by a quadratic polynomial with time-dependent coefficients,…
Reducibility of 1-D quantum harmonic oscillator with new unbounded oscillatory perturbations
Jin Xu, Jiawen Luo, Zhiqiang Wang +1
Enlightened by Lemma 1.7 in \cite{LiangLuo2021}, we prove a similar lemma which is based upon oscillatory integrals and Langer's turning point theory. From it we show that the Schr…
Growth of Sobolev Norms in 1-d Quantum Harmonic Oscillator with Polynomial Time Quasi-periodic Perturbation
Jiawen Luo, Zhenguo Liang, Zhiyan Zhao
We consider the one-dimensional quantum harmonic oscillator perturbed by a linear operator which is a polynomial of degree in , with coefficients quasi-…
Reducibility of 1-d Quantum Harmonic Oscillator Equation with Unbounded Oscillation Perturbations
Zhenguo Liang, Jiawen Luo
We build a new estimate relative with Hermite functions based upon oscillatory integrals and Langer's turning point theory. From it we show that the equation $$ i \partial_t u =-\p…
Three-dimensional solutions for the geostrophic flow in the Earth's core
Colin M. Hardy, Philip W. Livermore, Jitse Niesen +2
In his seminal work, Taylor (1963) argued that the geophysically relevant limit for dynamo action within the outer core is one of negligibly small inertia and viscosity in the magn…