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 ...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.展开更多
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 ph...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.展开更多
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 d...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.展开更多
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.
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 simu...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.展开更多
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)contain...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.展开更多
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 o...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.展开更多
文摘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.
基金Project supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDB22040502)the National Natural Science Foundation of China(No.11672285)and the Fundamental Research Funds for the Central Universities of China(No.WK2090050043)。
文摘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.
基金Supported by National Natural Science Foundation of China(Grant No.11671407 and 11701586)the Macao Science and Technology Development Fund(Grant No.0091/2018/A3)+1 种基金Guangdong Special Support Program(Grant No.8-2015)the key pro ject of NSF of Guangdong province(Grant No.2016A030311004)。
文摘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.
基金Supported by the National Natural Science Foundation of China 11331005,11201371,SRDPC20136101110015supported by the Natural Science Foundation of shaanxi province 2012JQ1020
文摘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.
基金supported by the Major Program of the National Natural Science Foundation of China(Grant No.11132008)
文摘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.
基金Supported by the National Natural Science Foundation of China(Grant No.12071043)the National Key Research and Development Program of China(Grant No.2020YFA0712900)。
文摘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.
基金Supported by the National Natural Science Foundation of China(Grant No.11471158)the Program for New Century Excellent Talents in University(Grant No.NCET-13–0857)the Fundamental Research Funds for the Central Universities(Grant No.NE2015005)
文摘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.