Zhang Lin | Searcharxiv

arXiv2014

Large time asymptotic behavior of the compressible Navier-Stokes Equations in partial Space-Periodic Domains

In this paper, we study the large time behavior of the 3-D isentropic compressible Navier-Stokes equation in the partial space-periodic domains, and simultaneously show that the related profile systems can be described by like Navier-Stokes equations with suitable "pressure" functions in lower dimensions. Our proofs are based on the energy methods together with some delicate analysis on the corresponding linearized problems.

math.AP↗

arXiv2010

All-derivable points in nest algebras

Suppose that $\mathscr{A}$ is an operator algebra on a Hilbert space $H$. An element $V$ in $\mathscr{A}$ is called an all-derivable point of $\mathscr{A}$ for the strong operator topology if every strong operator topology continuous derivable mapping $\phi$ at $V$ is a derivation. Let $\mathscr{N}$ be a complete nest on a complex and separable Hilbert space $H$. Suppose that $M$ belongs to $\mathscr{N}$ with $\{0\}\neq M\neq\ H$ and write $\hat{M}$ for $M$ or $M^{\bot}$. Our main result is: for any $\Omega\in alg\mathscr{N}$ with $\Omega=P(\hat{M})\Omega P(\hat{M})$, if $\Omega |_{\hat{M}}$ is invertible in $alg\mathscr{N}_{\hat{M}}$, then $\Omega$ is an all-derivable point in $alg\mathscr{N}$ for the strong operator topology.

math.OA↗