regularity

摘要： In this paper,we derive several new sufficient conditions of the non-breakdown of strong solutions for both the 3D heat-conducting compressible Navier-Stokes system and nonhomogeneous incompressible Navier-Stokes equations.First,it is shown that there exists a positive constantεsuch that the solution(ρ,u,θ)to the full compressible Navier-Stokes equations can be extended beyond t=T provided that one of the following two conditions holds:(1)ρ∈L^(∞)(0,T;L^(∞)(R^(3)),u∈L^(p,∞)(0,T;L^(q,∞)(R^(3)))and ||u||_(L^(p,∞)(0,T;L^(q,∞)(R^(3))))≤ε,with 2/p+3/q=1,q>3;(0.1)(2)λ3/2(0.2)To the best of our knowledge,this is the first continuation theorem allowing the time direction to be in Lorentz spaces for the compressible fluid.Second,we establish some blow-up criteria in anisotropic Lebesgue spaces for the finite blow-up time T^(*):(1)assuming that the pair(p,q) satisfies 2/p+1/q_(1)+1/q_(2)+1/q_(3)=1(1

摘要： [Objectives]The paper was to study the occurrence regularity and life history of cigarette beetle Lasioderrma serricorne(Fabricius)in tobacco leaf threshing and redrying workshop.[Methods]With the tobacco leaf threshing and redrying workshop as the survey site,the occurrence regularity of L.serricorne was investigated,and the life history table was inferred according to its biological characteristics.The temperature,humidity and duration of tobacco leaf threshing and redrying were simulated in the laboratory to study the survival rate of all states of L.serricorne in this environment.[Results]The lifecycle of L.serricorne in tobacco leaf threshing and redrying workshop was:the overwintering generation pupated in late February;the pupa began to emerge in early March,and reached its peak in late March.The first-generation eggs started hatching in late March,pupated in late May,emerged in early June,and reached the peak eclosion of the first-generation adults in mid-July.The second-generation eggs began to hatch in late July,pupated in mid-August,emerged in late August,and reached the peak eclosion of the second-generation adults in mid-September.The third-generation eggs began to hatch in mid-September;most of the larvae began to overwinter,some pupated in mid-November and survived the winter as pupae,and some pupae emerged to adults.The survival test results of different states of L.serricorne under simulated temperature,humidity and duration in the tobacco leaf threshing and redrying process showed that the mortality rates of eggs in simulated 1,2 and 3 conditions were about 51.22%,90.24% and 100%,and the mortalities of larvae in simulated 1,2 and 3 conditions were about 18.30%,81.25%and 100%,respectively.The mortalities of pupae in simulated 1,2 and 3 conditions were about 69.39%,100% and 100%,and the mortalities of adults in simulated 1,2 and 3 conditions were about 100%,100% and 100%,respectively.[Conclusions]L.serricorne of different states can be killed by appropriately raising the temperature during threshing and redrying.

摘要： Global climate governance is an important agenda for China in the face of the drastic changes unseen in a century After more than 30 years of hard work,China’s understanding of the regularity of global climate governance and logic of action both become clear.A new international competition with carbon neutrality as the goal has already begun in the trade-off between individual rationality and collective rationality China’s active participation in the process of global climate governance demonstrates its sense of responsibility as a major country.

摘要： This paper presents a very short solution to the 4th Millennium problem about the Navier-Stokes equations. The solution proves that there cannot be a blow up in finite or infinite time, and the local in time smooth solutions can be extended for all times, thus regularity. This happily is proved not only for the Navier-Stokes equations but also for the inviscid case of the Euler equations both for the periodic or non-periodic formulation and without external forcing (homogeneous case). The proof is based on an appropriate modified extension in the viscous case of the well-known Helmholtz-Kelvin-Stokes theorem of invariance of the circulation of velocity in the Euler inviscid flows. This is essentially a 1D line density of (rotatory) momentum conservation. We discover a similar 2D surface density of (rotatory) momentum conservation. These conservations are indispensable, besides to the ordinary momentum conservation, to prove that there cannot be a blow-up in finite time, of the point vorticities, thus regularity.

摘要： By using the nice behavior of the Hawking mass of the slices of a weak solution of inverse mean curvature flow in three-dimensional asymptotically hyperbolic manifolds, we are able to show that each slice of the flow is star-shaped after a long time, and then we get the regularity of the weak solution of inverse mean curvature flow in asymptotically hyperbolic manifolds. As an application, we prove that the limit of the Hawking mass of the slices of a weak solution of inverse mean curvature flow with any connected C^(2)-smooth surface as initial data in asymptotically anti-de Sitter-Schwarzschild manifolds with positive mass is greater than or equal to the total mass, which is completely different from the situation in the asymptotically flat case.

摘要： In this paper, we establish the global existence and uniqueness of the solution of the Cauchy problem of a one-dimensional compressible isentropic Euler system for a Chaplygin gas with large initial data in the space Lloc1. The hypotheses on the initial data may be the least requirement to ensure the existence of a weak solution in the Lebesgue measurable sense. The novelty and also the essence of the difficulty of the problem lie in the fact that we have neither the requirement on the local boundedness of the density nor that which is bounded away from vacuum. We develop the previous results on this degenerate system.The method used is Lagrangian representation, the essence of which is characteristic analysis.The key point is to prove the existence of the Lagrangian representation and the absolute continuity of the potentials constructed with respect to the space and the time variables.We achieve this by finding a property of the fundamental theorem of calculus for Lebesgue integration, which is a sufficient and necessary condition for judging whether a monotone continuous function is absolutely continuous. The assumptions on the initial data in this paper are believed to also be necessary for ruling out the formation of Dirac singularity of density. The ideas and techniques developed here may be useful for other nonlinear problems involving similar difficulties.

摘要： Background:Postoperative nausea and vomiting(PONV)refers to a problem commonly occurring after surgery.Acupuncture is considered a critical complementary alternative therapy for PONV.The acupoints selection critically determines the efficacy of acupuncture,whereas the selection rules remain unclear.The objective of the present study was to delve into the principles of acupoints selection for PONV using data mining technology.Methods:The clinical trials assessing the acupuncture effect for PONV were searched with the use of computer in PubMed,China National Knowledge Infrastructure,and Chinese Biomedical Database;the time span was confined as 2009–2019.The database of acupuncture prescriptions for PONV was built using Excel 2016;the description and association were analyzed by IBM SPSS modeler 18.Result:Eighty-three relevant literatures were screened out.The number of specific acupoints took up 72.5%of all acupoints;specific acupoints exhibited the frequency taking up 91.30%of the total frequency.As revealed from the result,Neiguan(PC 6),Zusanli(ST 36),Hegu(LI 4),and Zhongwan(CV 12)were most frequently applied,suggesting the tightest associations.Most acupoints were taken from the stomach meridian and pericardium meridian.The common acupoints were concentrated in the lower limbs,chest,as well as abdomen.Conclusion:Data mining acts as a feasible method to identify acupoints selection and compatibility characteristics.As suggested from our study,the acupoints selection for PONV prioritizes specific acupoints and related meridians.The selection and combination of acupoints comply with the theory of traditional Chinese medicine.

摘要： In this paper,we investigate the regularity criterion via the pressure of weak solutions to the micropolar fluid equations in three dimensions.We obtain that for 0<α<1 if p€L^(2/a)(0,T;B^α∞,∞),then the weak solution(u,ω)is regular on(0,T).

摘要： In this paper,a special case of nonlinear time fractional cable equation is studied.For the equation defined on a bounded domain,the existence,uniqueness,and regularity of the solution are firstly studied.Furthermore,it is numerically studied via the weighted and shifted Grünwald difference(WSGD)methods/the local discontinuous Galerkin(LDG)finite element methods.The derived numerical scheme has been proved to be stable and convergent with order O(
t2+hk+1),where
t,h,k are the time stepsize,the spatial stepsize,and the degree of piecewise polynomials,respectively.Finally,a numerical experiment is presented to verify the theoretical analysis.