WELL-POSEDNESS IN CRITICAL SPACES FOR THE FULL COMPRESSIBLE MHD EQUATIONS

In this paper we prove local well-posedness in critical Besov spaces for the full compressible MHD equations in R^N, N≥ 2, under the assumptions that the initialdensity is bounded away from zero. The proof relies on uniform estimates for a mixed hyperbolic/parabolic linear system with a convection term.

Elastic interaction between inclusions and tunable periodicity of superlattice structure in nanowires

The elastic stress distribution and the variation of the elastic energy with spacing between two inclusions of arbitrary sizes in an infinite isotropic cylindrical rod are obtained by an analytical approach and the phase field microelasticity(PFM)simulation.The results show a near-attraction and far-repulsion elastic interaction between two inclusions with hydrostatic dilatation.The critical spacing,at which the interaction changes from attraction to repulsion,is on the order of the radius of the rod,dependent on the length and Poisson’s ratio of inclusions.Furthermore,the elastic energy calculations and PFM simulation results indicate that applying the local radial stress on the rod surface can modulate the elastic interaction between inclusions and adjust the periodicity of the superlattice nanowire structure.This can provide some guidelines for the tunable construction of superlattice nanowire structures.

Stability of solutions for nonlinear Schrdinger equations in critical spaces

We consider the Cauchy problem for nonlinear Schrdinger equation iut + Δu = ±|u|pu,4/d< p <4 /d-2 in high dimensions d 6. We prove the stability of solutions in the critical space H˙xsp , where sp = d/2-p/2 .

Global Well-posedness for the Non-viscous MHD Equations with Magnetic Diffusion in Critical Besov Spaces

In this paper,we mainly investigate the Cauchy problem of the non-viscous MHD equations with magnetic diffusion.We first establish the local well-posedness(existence,uniqueness and continuous dependence)with initial data(u_(0),b_(0))in critical Besov spaces B_(p,1)^(d/p+1)×B_(p,1)^(d/p)with 1≤p≤∞,and give a lifespan T of the solution which depends on the norm of the Littlewood–Paley decomposition(profile)of the initial data.Then,we prove the global existence in critical Besov spaces.In particular,the results of global existence also hold in Sobolev space C([0,∞);H~s(S~2))×(C([0,∞);H^(s-1)(S~2))∩L~2([0,∞);H~s(S~2)))with s>2,when the initial data satisfies∫_(S~2)b_(0)dx=0 and||u_(0)||B_(()∞,1~((S~2)))~1+||b_(0)||B_(()∞,1^(S~2))~0≤ε.It’s worth noting that our results imply some large and low regularity initial data for the global existence.

On the Local Wellposedness of Three-dimensional MHD System in the Critical Spaces

In this article, we prove the local wellposedness of Three-Dimensional incompressible magnetohydrodynamic system（MHD） with initial data in the critical spaces, without assumptions of small density variation.

The inviscid limit for the Landau-Lifshitz-Gilbert equation in the critical Besov space

We prove that in dimensions three and higher the Landau-Lifshitz-Gilbert equation with small initial data in the critical Besov space is globally well-posed in a uniform way with respect to the Gilbert damping parameter. Then we show that the global solution converges to that of the Schr¨odinger maps in the natural space as the Gilbert damping term vanishes. The proof is based on some studies on the derivative Ginzburg-Landau equations.

WALL EFFECTS ON FLOWS PAST TWO TANDEM CYLINDERS OF DIFFERENT DIAMETERS

Flows past two tandem cylinders of different diameters placed centrally in a channel with fixed centre-to-centre spacing 6D and diameter ratio are simulated based on the Lattice Boltzmann Method（LBM）.In all the simulations,the diameter of the smaller cylinder is chosen as the characteristic length.The Reynolds number based on the average inflow velocity is 20-120 and studies are over the range of blockage ratio 2-8.In both Small-Big Arrangement（SBA）and Big-Small Arrangement（BSA）,the effects of the channel width and Reynolds number on the flow structures and force coefficients are studied.Results show that the flows in BSA are more regular than those in SBA for the same flow fields.In BSA with and,the force coefficients all fluctuate with constant amplitudes and a coupled frequency,the coupled frequency becomes small as the blockage ratio decreases and by an exact test we give out the relation of the blockage ratio and Strouhal number.As the blockage ratio decreases to 2,there exist pitchfork bifurcations in both SBA and BSA,and results show that the critical Reynolds numbers of pitchfork bifurcations for SBA and BSA are both between 60 and 80.In SBA with,the flow structure has a static asymmetric mode.It is found that the channel width has also an effect on the critical spacing where the flow changes from single body mode into co-shedding mode.By an accurate survey on flows past two cylinders with equal diameters placed inside a channel with the width,the relation between channel width and the critical spacing is given and results show that the critical spacing increases as the channel width increases.

SPECIAL ISSUE： SPACE PRODUCTION AND URBAN ORDER IN CONTEMPORARY CHINA--From Object to Perspective： A Shift of Significance in Space Production and Space Criticism--The Issue of Space in Conceptualizing Contemporary Chinese Urban Construction

Physical space refers to both natural space and social space, that is, social relations. Space production includes production in space and of space. Relations between these two dimensions and between physical space production and social space production constitute two basic relations in space production. The dialectical connotation of these two basic relations manifests the truth that space production can basically be summed up as reproduction of social relations. Therefore, arguments about space production can be seen as involving a fundamental shift of importance from object to perspective. Seen in this way, there remain some errors in ideas about today＇s Chinese urban construction, that is, the rupture and separation of object and perspective, resulting in unnecessary risks and costs in the progress of modem Chinese ttrbanization.

Global Fujita-Kato's Type Solutions and Long-time Behavior for the Multidimensional Chemotaxis Model

We establish the global well-posedness for the multidimensional chemotaxis model with some classes of large initial data,especially the case when the rate of variation of ln v0(v0 is the chemical concentration)contains high oscillation and the initial density near the equilibrium is allowed to have large oscillation in 3D.Besides,we show the optimal time-decay rates of the strong solutions under an additional perturbation assumption,which include specially the situations of d=2,3 and improve the previous time-decay rates.Our method mainly relies on the introduce of the effective velocity and the application of the localization in Fourier spaces.

A Note on Time-Decay Estimates for the Compressible Navier–Stokes Equations

In the recent work, we have developed a decay framework in general Lp critical spaces and established optimal time-decay estimates for barotropic compressible Navier-Stokes equations. Those decay rates of Lq-Lr type of the solution and its derivatives are available in the critical regularity framework, which were exactly firstly observed by Matsumura ＆ Nishida, and subsequently generalized by Ponce for solutions with high Sobolev regularity. We would like to mention that our approach is likely to be effective for other hyperbolic/parabolic systems that are encountered in fluid mechanics or mathematical physics. In this paper, a new observation is involved in the high frequency, which enables us to improve decay exponents for the high frequencies of solutions.