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Chun Ho Lau

Publications and source records attributed to Chun Ho Lau.

9 recordsLinked to original sources
arXiv2026

Periodic solution and its stability of a damped BBM equation posed on $\mathbb{T}$

In this paper, we are concerned with the existence and stability of temporal periodic solutions to a class of the Benjamin-Bona-Mahony (BBM) equation with damping in the torus $\mathbb{T}$, whose interior is applied with periodic force $f(x, t)$ with temporal period $θ$. These types of solutions are established in $H^{\ell}, \ell\ge 0$, and it is noteworthy to see that the I-energy method is invoked when low regularity of $\ell\in[0, 1)$ is pursued.

math.AP↗
arXiv2026

Forced oscillation of a damped BBM equation posed on whole line in low regularity spaces

In this manuscript, we would established in low regularity spaces $H^\ell, \ell\in [0,1)$, the existence and stability results of time-periodic solution of 1D Cauchy problem of forced damped Benjamin-Bona-Mahony equation (BBM). We use estimates from I-energy method to derive needed estimates in $H^\ell$ for the linearized problem, then convection term will be treated as perturbation of linear problem such that original Cauchy problem is solved.

math.AP↗
arXiv2025

On periodic solutions of the Benjamin-Bona-Mahony-Burgers equation

In this paper, we would establish the existence and stability of periodic solutions to the Benjamin-Bona-Mahony-Burgers (BBM-Burgers) equation in $H^1_0([0, 1])$, whose medium interior is applied with time-periodic force $f(x, t)$ with period $θ$. High regularity analysis has been conducted in Hilbert spaces $H^\ell, \ell>1$. We also consider periodic solution to same IBVP scenario of a pseudo-parabolic-regularized equation as an extension of the BBM-Burgers in $\mathcal{H}^{\ell}, \ell=\{1, 2\}$.

math.AP↗
arXiv2025

On the kernel conditions of operators mapping atoms to molecules in local Hardy spaces

In this paper, we explore the relationship between the operators mapping atoms to molecules in local Hardy spaces $h^p(\mathbb{R}^n)$ and the size conditions of its kernel. In particular, we show that if the kernel of a Calderón--Zygmund-type operator satisfies an integral-type size condition and a $T^*-$type cancellation, then the operator maps $h^p(\mathbb{R}^n)$ atoms to molecules. On the other hand, assuming that $T$ is an integral type operator bounded on $L^2(\mathbb{R}^n)$ that maps atoms to molecules in $h^p(\mathbb{R}^n)$, then the kernel of such operator satisfies the same integral-type size conditions. We also provide the $L^1(\mathbb{R}^n)$ to $L^{1,\infty}(\mathbb{R}^n)$ boundedness for such operators connecting our integral-type size conditions on the kernel with others presented in the literature.

math.CA↗
arXiv2024

Restriction of Fractional Derivatives of the Fourier Transform

In this paper, we showed that for suitable $(β,p, s,\ell)$ the $β$-order fractional derivative with respect to the last coordinate of the Fourier transform of an $L^p(\mathbb{R}^n)$ function is in $H^{-s}$ after restricting to a graph of a function with non-vanishing Gaussian curvature provided that the restriction of the Fourier transform of such function to the surface is in $H^{\ell}$. This is a generalization of the result in \cite{GoldStol}*{Theorem 1.12}.

math.FA↗
arXiv2023

$h^1$ boundedness of Localized Operators and Commutators with bmo and lmo

We first consider two types of localizations of singular integral operators of convolution type, and show, under mild decay and smoothness conditions on the auxiliary functions, that their boundedness on the local Hardy space $h^1(\mathbb{R}^n)$ is equivalent. We then study the boundedness on $h^1(\mathbb{R}^n)$ of the commutator $[b,T]$ of an inhomogeneous singular integral operator with $b$ in $bmo(\mathbb{R}^n)$, the nonhomogeneous space of functions of bounded mean oscillation. We define local analogues of the atomic space $H^1_b(\mathbb{R}^n)$ introduced by Pérez in the case of the homogeneous Hardy space and $BMO$, including a variation involving atoms with approximate cancellation conditions. For such an atom $a$, we prove integrability of the associated commutator maximal function and of $[b,T](a)$. For $b$ in $lmo(\mathbb{R}^n)$, this gives $h^1$ to $L^1$ boundedness of $[b,T]$. Finally, under additional approximate cancellation conditions on $T$, we show boundedness to $h^1$.

math.FA↗
arXiv2022

Necessary cancellation conditions for the boundedness of operators on local Hardy spaces

In this work we present necessary cancellation conditions for the continuity of linear operators in $h^p(\mathbb{R}^n)$, $0<p\leq 1$, that map atoms into pseudo-molecules. Our necessary condition, expressed in terms of the $T^{\ast}$ condition, is the same as the one recently proved sufficient in [3], thus providing a necessary and sufficient cancellation condition for the boundedness of inhomogeneous Calderón--Zygmund type operators

math.AP↗
arXiv2022

Periodic measures for a class of SPDEs with regime-switching

We use the variational approach to investigate periodic measures for a class of SPDEs with regime-switching. The hybrid system is driven by degenerate Lévy noise. We use the Lyapunov function method to study the existence of periodic measures and show the uniqueness of periodic measures by establishing the strong Feller property and irreducibility of the associated time-inhomogeneous semigroup. The main results are applied to stochastic porous media equations with regime-switching.

math.PR↗