In this article the author considers Cauchy problem for one dimensional Navier Stokes equations and the global smooth resolvablity for classical solutions is obtained.
The author considers the Cauchy problem for quasilinear inhomogeneous hyperbolic systems.Under the assumption that the system is weakly dissipative,Hanouzet and Natalini established the global existence of smooth solu...The author considers the Cauchy problem for quasilinear inhomogeneous hyperbolic systems.Under the assumption that the system is weakly dissipative,Hanouzet and Natalini established the global existence of smooth solutions for small initial data (in Arch.Rational Mech.Anal.,Vol.169,2003,pp.89-117).The aim of this paper is to give a completely different proof of this result with slightly different assumptions.展开更多
For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissipation,the globa...For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissipation,the global existence of H 2 classical solution to the Cauchy problem with small initial data is obtained.展开更多
The economic benefits of insect-resistant genetically modified(GM) crops have been well documented, but the impact of such crops and the consequent reduction in pesticide use on farmers' health remains largely unk...The economic benefits of insect-resistant genetically modified(GM) crops have been well documented, but the impact of such crops and the consequent reduction in pesticide use on farmers' health remains largely unknown. Through the analysis of the data collected from the physical examination from farmers in China, we show that GM rice significantly reduces pesticide use and the resultant not only visible but also invisible adverse effects on farmers' neurological, hematological, and electrolyte system. Hence, the commercialization of GM rice is expected to improve the health of farmers in developing countries, where pesticide application is necessary to mitigate crop loss.展开更多
We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the isentropic compressible Navier-Stokes equations in the three space dimensions with general initial data which could...We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the isentropic compressible Navier-Stokes equations in the three space dimensions with general initial data which could be either vacuum or non-vacuum under the assumption that the viscosity coefficient μ is large enough.展开更多
In this paper, we prove local and global existence of classical solutions for a system of equations concerning an incompressible viscoelastic fluid of Oldroyd-B type via the incompressible limit when the initial data ...In this paper, we prove local and global existence of classical solutions for a system of equations concerning an incompressible viscoelastic fluid of Oldroyd-B type via the incompressible limit when the initial data are sufficiently small.展开更多
In this paper we study the global existence and uniqueness of classical solutions to the Cauchy problem for 3D isentropic compressible Navier-Stokes equations with general initial data which could contain vacuum.We gi...In this paper we study the global existence and uniqueness of classical solutions to the Cauchy problem for 3D isentropic compressible Navier-Stokes equations with general initial data which could contain vacuum.We give the relation between the viscosity coefficients and the initial energy,which implies that the Cauchy problem under consideration has a global classical solution.展开更多
文摘In this article the author considers Cauchy problem for one dimensional Navier Stokes equations and the global smooth resolvablity for classical solutions is obtained.
基金Project supported by the National Natural Science Foundation of China (No. 10728101)the Basic Research Program of China (No. 2007CB814800)+1 种基金the Doctoral Program Foundation of the Ministry of Education of Chinathe "111" Project (No. B08018) and SGST (No. 09DZ2272900)
文摘The author considers the Cauchy problem for quasilinear inhomogeneous hyperbolic systems.Under the assumption that the system is weakly dissipative,Hanouzet and Natalini established the global existence of smooth solutions for small initial data (in Arch.Rational Mech.Anal.,Vol.169,2003,pp.89-117).The aim of this paper is to give a completely different proof of this result with slightly different assumptions.
基金supported by the Fudan University Creative Student Cultivation Program in Key Disciplinary Areas (No. EHH1411208)
文摘For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissipation,the global existence of H 2 classical solution to the Cauchy problem with small initial data is obtained.
基金supported by the International Development Research Center(106160-002)the National Natural Science Foundation of China(71333013,71210004)National Key Program on Genetically Modified New Varieties(2011ZX08015-002A)
文摘The economic benefits of insect-resistant genetically modified(GM) crops have been well documented, but the impact of such crops and the consequent reduction in pesticide use on farmers' health remains largely unknown. Through the analysis of the data collected from the physical examination from farmers in China, we show that GM rice significantly reduces pesticide use and the resultant not only visible but also invisible adverse effects on farmers' neurological, hematological, and electrolyte system. Hence, the commercialization of GM rice is expected to improve the health of farmers in developing countries, where pesticide application is necessary to mitigate crop loss.
基金supported by National Natural Science Foundation of China (Grant No.11001090)the Fundamental Research Funds for the Central Universities (Grant No. 11QZR16)
文摘We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the isentropic compressible Navier-Stokes equations in the three space dimensions with general initial data which could be either vacuum or non-vacuum under the assumption that the viscosity coefficient μ is large enough.
基金Project supported by the National Natural Science Foundation of China (No. 10225102)the 973 Project of the Ministry of Science and Technology of China and the Doctoral Program Foundation of the Ministry of Education of China.
文摘In this paper, we prove local and global existence of classical solutions for a system of equations concerning an incompressible viscoelastic fluid of Oldroyd-B type via the incompressible limit when the initial data are sufficiently small.
基金supported by National Natural Science Foundation of China (Grant Nos.11001090 and 10971171)the Fundamental Research Funds for the Central Universities (Grant No.11QZR16)
文摘In this paper we study the global existence and uniqueness of classical solutions to the Cauchy problem for 3D isentropic compressible Navier-Stokes equations with general initial data which could contain vacuum.We give the relation between the viscosity coefficients and the initial energy,which implies that the Cauchy problem under consideration has a global classical solution.