arXiv subjects

Ting Zhang

Publications and source records attributed to Ting Zhang.

245 records · Page 14Linked to original sources

arXiv2011

Global existence in critical spaces for incompressible viscoelastic fluids

We investigate local and global strong solutions for the incompressible viscoelastic system of Oldroyd--B type. We obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations. More precisely, the initial velocity has the same critical regularity index as for the incompressible Navier--Stokes equations, and one more derivative is needed for the deformation tensor. We point out a smoothing effect on the velocity and a $L^1-$decay on the difference between the deformation tensor and the identity matrix. Our result implies that the deformation tensor $F$ has the same regularity as the density of the compressible Navier--Stokes equations.

math.AP↗

arXiv2009

1D goes 2D: A Kosterlitz Thouless transition in superconducting arrays of 4-Angstrom carbon nanotubes

We report superconducting resistive transition characteristics for array(s) of coupled 4-Angstrom single wall carbon nanotubes embedded in aluminophosphate-five (AFI) zeolite. The transition was observed to initiate at 15K with a slow resistance decrease switching to a sharp, order of magnitude drop between 7.5-6.0K. The transition has strong (anisotropic) magnetic field dependence. Differential resistance versus current (voltage) measurements indicate that the establishment of coherence proceeds in stages as the temperature is lowered below 15K. In particular, the sharp resistance drop and its attendant nonlinear IV characteristics are consistent with the manifestations of a Kosterlitz-Thouless (KT) transition that establishes quasi long range order in the plane transverse to the c-axis of the nanotubes, leading to an inhomogeneous system comprising 3D superconducting regions connected by weak links. Global coherence is established at below 5K with the appearance of a well-defined supercurrent gap at 2K.

cond-mat.supr-con↗

arXiv2009

Global solutions of compressible Navier-Stokes equations with a density-dependent viscosity coefficient

We prove the global existence and uniqueness of the classical (weak) solution for the 2D or 3D compressible Navier-Stokes equations with a density-dependent viscosity coefficient ($λ=λ(ρ)$). Initial data and solutions are only small in the energy-norm. We also give a description of the large time behavior of the solution. Then, we study the propagation of singularities in solutions. We obtain that if there is a vacuum domain at initially, then the vacuum domain will exists for all time, and vanishes as time goes to infinity.

math.AP↗

arXiv2009

Compressible flows with a density-dependent viscosity coefficient

We prove the global existence of weak solutions for the 2-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient ($λ=λ(ρ)$). Initial data and solutions are small in energy-norm with nonnegative densities having arbitrarily large sup-norm. Then, we show that if there is a vacuum domain at the initial time, then the vacuum domain will retain for all time, and vanishes as time goes to infinity. At last, we show that the condition of $μ=$constant will induce a singularity of the system at vacuum. Thus, the viscosity coefficient $μ$ plays a key role in the Navier-Stokes equations.

math.AP↗

arXiv2008

Global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations

In this paper, we consider a global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations (\textit{ANS}). In order to do so, we first introduce the scaling invariant Besov-Sobolev type spaces, $B^{-1+\frac{2}{p},{1/2}}_{p}$ and $B^{-1+\frac{2}{p},{1/2}}_{p}(T)$, $p\geq2$. Then, we prove the global wellposedness for (\textit{ANS}) provided the initial data are sufficient small compared to the horizontal viscosity in some suitable sense, which is stronger than $B^{-1+\frac{2}{p},{1/2}}_{p}$ norm. In particular, our results imply the global wellposedness of (\textit{ANS}) with high oscillatory initial data.

math.AP↗

arXiv2008

A vacuum problem for multidimensional compressible Navier-Stokes equations with degenerate viscosity coefficients

Local solutions of the multidimensional Navier-Stokes equations for isentropic compressible flow are constructed with spherically symmetric initial data between a solid core and a free boundary connected to a surrounding vacuum state. The viscosity coefficients $λ, μ$ are proportional to $ρ^θ}$, $0<θ<γ$, where $ρ$ is the density and $γ>1$ is the physical constant of polytropic fluid. It is also proved that no vacuum develops between the solid core and the free boundary, and the free boundary expands with finite speed.

math.AP↗

arXiv2007

A note on spherically symmetric isentropic compressible flows with density-dependent viscosity coefficients

In this note, by constructing suitable approximate solutions, we prove the existence of global weak solutions to the compressible Navier-Stokes equations with density-dependent viscosity coefficients in the whole space $\mathbb{R}^N$, $N\geq2$ (or exterior domain), when the initial data are spherically symmetric. In particular, we prove the existence of spherically symmetric solutions to the Saint-Venant model for shallow water in the whole space (or exterior domain).

math.AP↗

arXiv2007

Global exponential stability of classical solutions to the hydrodynamic model for semiconductors

In this paper, the global well-posedness and stability of classical solutions to the multidimensional hydrodynamic model for semiconductors on the framework of Besov space are considered. We weaken the regularity requirement of the initial data, and improve some known results in Sobolev space. The local existence of classical solutions to the Cauchy problem is obtained by the regularized means and compactness argument. Using the high- and low- frequency decomposition method, we prove the global exponential stability of classical solutions (close to equilibrium). Furthermore, it is also shown that the vorticity decays to zero exponentially in the 2D and 3D space. The main analytic tools are the Littlewood-Paley decomposition and Bony's para-product formula.

math.AP↗

arXiv2007

Global Behavior of Spherically Symmetric Navier-Stokes Equations with Degenerate Viscosity Coefficients

In this paper, we study a free boundary problem for compressible spherically symmetric Navier-Stokes equations with a gravitational force and degenerate viscosity coefficients. Under certain assumptions that imposed on the initial data, we obtain the global existence and uniqueness of the weak solution and give some uniform bounds (with respect to time) of the solution. Moreover, we obtain some stabilization rate estimates in $L^\infty$-norm and weighted $H^1$-norm of the solution. The results show that such system is stable under the small perturbations, and could be applied to the astrophysics.

math.AP↗

arXiv2007

Global Behavior of Spherically Symmetric Navier-Stokes Equations with Density-Dependent Viscosity

In this paper, we study a free boundary problem for compressible spherically symmetric Navier-Stokes equations without a solid core. Under certain assumptions imposed on the initial data, we obtain the global existence and uniqueness of the weak solution, give some uniform bounds (with respect to time) of the solution and show that it converges to a stationary one as time tends to infinity. Moreover, we obtain the stabilization rate estimates of exponential type in $L^\infty$-norm and weighted $H^1$-norm of the solution by constructing some Lyapunov functionals. The results show that such system is stable under the small perturbations, and could be applied to the astrophysics.

math.AP↗

arXiv2007

Existence and uniqueness results for viscous, heat-conducting 3-D fluid with vacuum

We consider the 3-D full Navier-Stokes equations whose the viscosity coefficients and the thermal conductivity coefficient depend on the density and the temperature. We prove the local existence and uniqueness of the strong solution in a domain $Ω\subset\mathbb{R}^3$. The initial density may vanish in an open set and $Ω$ could be a bounded or unbounded domain. We also prove a blow-up criterion for the solution. Finally, we show the blow-up of the smooth solution to the compressible Navier-Stokes equations in $\mathbb{R}^n$ ($n\geq1$) when the initial density has compactly support and the initial total momentum is nonzero.

math.AP↗