arXiv subjects

Jianwen Zhang

Publications and source records attributed to Jianwen Zhang.

23 records · Page 2Linked to original sources

arXiv2012

Global well-posedness for the two-dimensional equations of nonhomogeneous incompressible liquid crystal flows with nonnegative density

In this paper, the authors first establish the global well-posedness of strong solutions of the simplified Ericksen-Leslie model for nonhomogeneous incompressible nematic liquid crystal flows in two dimensions if the initial data satisfies some smallness condition. It is worth pointing out that the initial density is allowed to contain vacuum states and the initial velocity can be arbitrarily large. We also present a Serrin's type criterion, depending only on $\nabla d$, for the breakdown of local strong solutions. As a byproduct, the global strong solutions with large initial data are obtained, provided the macroscopic molecular orientation of the liquid crystal materials satisfies a natural geometric angle condition (cf. [19])

math.AP↗

arXiv2012

Global Well-Posedness with Large Oscillations and Vacuum to the Three-Dimensional Equations of Compressible Nematic Liquid Crystal Flows

This paper is concerned with the three-dimensional equations of a simplified hydrodynamic flow modeling the motion of compressible, nematic liquid crystal materials. The authors establish the global existence of classical solution to the Cauchy problem with smooth initial data which are of small energy but possibly large oscillations with constant state as far-field condition which could be either vacuum or non-vacuum. The initial density is allowed to vanish and the spatial measure of the set of vacuum can be arbitrarily large, in particular, the initial density can even have compact support. As a byproduct, the large-time behavior of the solution is also studied.

math.AP↗

arXiv2011

On the motion of three-dimensional compressible isentropic flows with large external potential forces and vacuum

We study the global existence and uniqueness of classical solutions to the three-dimensional compressible isentropic Navier-Stokes equations with vacuum and external potential forces which could be arbitrarily large provided the initial data is of small energy and the unique steady state is strictly away from vacuum. In particular, the solution may have large oscillations and contain vacuum states. For the case of discontinuous initial data, we also prove the global existence of weak solutions. The large-time behavior of the solution is obtained simultaneously. It is worthwhile mentioning that the compatibility condition on the initial data and the regularity condition of the external potential forces in the present paper are much weaker than those assumed in the existing literature.

math.AP↗

arXiv2007

Nearly MDS expander codes with reduced alphabet size

Recently, Roth and Skachek proposed two methods for constructing nearly maximum-distance separable (MDS) expander codes. We show that through the simple modification of using mixed-alphabet codes derived from MDS codes as constituent codes in their code designs, one can obtain nearly MDS codes of significantly smaller alphabet size, albeit at the expense of a (very slight) reduction in code rate.

cs.IT↗

arXiv2006

Retrieving Reed-Solomon coded data under interpolation-based list decoding

A transform that enables generator-matrix-based Reed-Solomon (RS) coded data to be recovered under interpolation-based list decoding is presented. The transform matrix needs to be computed only once and the transformation of an element from the output list to the desired RS coded data block incurs $k^{2}$ field multiplications, given a code of dimension $k$.

cs.IT↗