arXiv subjects

Wengu Chen

Publications and source records attributed to Wengu Chen.

25 records · Page 2Linked to original sources

arXiv2016

Recovery of signals under the condition on RIC and ROC via prior support information

In this paper, the sufficient condition in terms of the RIC and ROC for the stable and robust recovery of signals in both noiseless and noisy settings was established via weighted $l_{1}$ minimization when there is partial prior information on support of signals. An improved performance guarantee has been derived. We can obtain a less restricted sufficient condition for signal reconstruction and a tighter recovery error bound under some conditions via weighted $l_{1}$ minimization. When prior support estimate is at least $50\%$ accurate, the sufficient condition is weaker than the analogous condition by standard $l_{1}$ minimization method, meanwhile the reconstruction error upper bound is provably to be smaller under additional conditions. Furthermore, the sufficient condition is also proved sharp.

cs.IT↗

arXiv2009

Global well-posedness and I-method for the fifth-order Korteweg-de Vries equation

We prove that the Kawahara equation is locally well-posed in $H^{-7/4}$ by using the ideas of $\bar{F}^s$-type space \cite{GuoKdV}. Next we show it is globally well-posed in $H^s$ for $s\geq -7/4$ by using the ideas of "I-method" \cite{I-method}. Compared to the KdV equation, Kawahara equation has less symmetries, such as no invariant scaling transform and not completely integrable. The new ingredient is that we need to deal with some new difficulties that are caused by the lack symmetries of this equation.

math.AP↗

arXiv2009

Sharp Well-posedness for the Benjamin Equation

Having the ill-posedness in the range $s<-3/4$ of the Cauchy problem for the Benjamin equation with an initial $H^{s}({\mathbb R})$ data, we prove that the already-established local well-posedness in the range $s>-3/4$ of this initial value problem is extendable to $s=-3/4$ but also that such a well-posed property is globally valid for $s\in [-3/4,\infty)$.

math.AP↗

arXiv2009

A Sharp Bilinear Estimate for the Bourgain-type Space with Application to the Benjamin Equation

This note shows the existence of a sharp bilinear estimate for the Bourgain-type space and gives its application to the optimal local well/ill-posedness of the Cauchy problem for the Benjamin equation.

math.AP↗

arXiv2009

Low regularity solutions of two fifth-order KdV type equations

The Kawahara and modified Kawahara equations are fifth-order KdV type equations and have been derived to model many physical phenomena such as gravity-capillary waves and magneto-sound propagation in plasmas. This paper establishes the local well-posedness of the initial-value problem for Kawahara equation in $H^s({\mathbf R})$ with $s>-\frac74$ and the local well-posedness for the modified Kawahara equation in $H^s({\mathbf R})$ with $s\ge-\frac14$. To prove these results, we derive a fundamental estimate on dyadic blocks for the Kawahara equation through the $[k; Z]$ multiplier norm method of Tao \cite{Tao2001} and use this to obtain new bilinear and trilinear estimates in suitable Bourgain spaces.

math.AP↗

arXiv2008

On the low regularity of the fifth order Kadomtsev-Petviashvili I equation

We consider the fifth order Kadomtsev-Petviashvili I (KP-I) equation as $\partial_tu+α\partial_x^3u+\partial^5_xu+\partial_x^{-1}\partial_y^2u+uu_x=0,$ while $α\in \mathbb{R}$. We introduce an interpolated energy space $E_s$ to consider the well-posedeness of the initial value problem (IVP) of the fifth order KP-I equation. We obtain the local well-posedness of IVP of the fifth order KP-I equation in $E_s$ for $0<s\leq1$. To obtain the local well-posedness, we present a bilinear estimate in the Bourgain space in the framework of the interpolated energy space. It crucially depends on the dyadic decomposed Strichartz estimate, the fifth order dispersive smoothing effect and maximal estimate. Key words: The fifth order KP-I equation, Bourgain space, Dyadic decomposed Strichartz estimate, Dispersive smoothing effect, Maximal estimate.

math.AP↗

arXiv2007

The well-posedness of Cauchy problem for dissipative modified Korteweg de Vries equations

In this paper we consider some dissipative versions of the modified Korteweg de Vries equation $u_t+u_{xxx}+|D_x|^αu+u^2u_x=0$ with $0<α\leq 3$. We prove some well-posedness results on the associated Cauchy problem in the Sobolev spaces $H^s({\Bbb R})$ for $s>1/4-α/4$ on the basis of the $[k; Z]-$multiplier norm estimate obtained by Tao in \cite{Tao} for KdV equation.

math.AP↗