arXiv subjects

Vu Thanh Nguyen

Publications and source records attributed to Vu Thanh Nguyen.

3 recordsLinked to original sources

arXiv2023

3D Navier-Stokes Equations with Nonvanishing Boundary Condition

This paper investigates the existence and regularity of strong solutions to the incompressible Navier-Stokes equations within a bounded domain $Ω\subset \mathbb{R}^3$, subject to the boundary condition $(u\cdot \vec{n})|_{\partial Ω}=0$. Here, $\vec{n}$ represents the normal vector to the boundary $\partialΩ$, and the equation is given by $\partial_t u = νΔu - (u \cdot \nabla) u - \nabla p + f$, with initial condition $u|_{t=0}=u_o\in H$ and the divergence constraint $div\,u = 0$. This paper aims to establish the existence and the regularity of local-in-time strong solutions when the boundary condition is $(u\cdot \vec{n})|_{\partial Ω}=0$.

math.AP↗

arXiv2023

Non-uniqueness of solutions for 3D Navier-Stokes equations in bounded domains

This paper examines the uniqueness/non-uniqueness of local-in-time strong solutions for the incompressible 3D Navier-Stokes equations in bounded domains, which are $\partial_t u=νΔu- u\cdot \nabla u-\nabla p+ f$ and $div~u=0$. The focus of this study is on the case where the boundary condition is defined as $u\cdot \vec{n}|_{\partialΩ}=0$. This paper demonstrates the existence of two distinct strong solutions to the Navier-Stokes equations under this boundary condition.

math.AP↗

arXiv2009

Using social annotation and web log to enhance search engine

Search services have been developed rapidly in social Internet. It can help web users easily to find their documents. So that, finding a best method search is always an imagine. This paper would like introduce hybrid method of LPageRank algorithm and Social Sim Rank algorithm. LPageRank is the method using link structure to rank priority of page. It doesn't care content of page and content of query. Therefore, we want to use benefit of social annotations to create the latent semantic association between queries and annotations. This model, we use algorithm SocialPageRank and LPageRank to enhance accuracy of search system. To experiment and evaluate the proposed of the new model, we have used this model for Music Machine Website with their web logs.

cs.IR↗