The solvability of the fifth-order nonlinear dispersive equation δtu＋au （δxu）^2＋βδx^3u＋γδx^5u = 0 is studied. By using the approach of Kenig, Ponce and Vega and some Strichartz estimates for the correspondi...The solvability of the fifth-order nonlinear dispersive equation δtu＋au （δxu）^2＋βδx^3u＋γδx^5u = 0 is studied. By using the approach of Kenig, Ponce and Vega and some Strichartz estimates for the corresponding linear problem,it is proved that if the initial function u0 belongs to H^5（R） and s〉1/4,then the Cauchy problem has a unique solution in C（[-T,T],H^5（R）） for some T〉0.展开更多
In this paper, we study the initial-boundary value problem with rigid wall for the equations in combustion dynamics with largy parameter. Introducing variable scalar norms and two seminorms, making use of the vorticit...In this paper, we study the initial-boundary value problem with rigid wall for the equations in combustion dynamics with largy parameter. Introducing variable scalar norms and two seminorms, making use of the vorticity operator, overcome the difficulty from the large parameter. By energy estimation, the existence and unique theorems of local smooth solution is proved.展开更多
The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods.Furthermore the connection between the model and an anharmonic oscillator is investigated by methods of KStra...The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods.Furthermore the connection between the model and an anharmonic oscillator is investigated by methods of KStransformation.展开更多
In this work, we present final solving Millennium Prize Problems formulated by Clay Math. Inst., Cambridge. A new uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided. We ...In this work, we present final solving Millennium Prize Problems formulated by Clay Math. Inst., Cambridge. A new uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided. We also describe the loss of smoothness of classical solutions for the Navier-Stokes equations.展开更多
The analytic properties of the scattering amplitude are discussed, and a representation of the potential is obtained using the scattering amplitude. A uniform time estimation of the Cauchy problem solution for the Nav...The analytic properties of the scattering amplitude are discussed, and a representation of the potential is obtained using the scattering amplitude. A uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided. The paper also describes the time blowup of classical solutions for the Navier-Stokes equations by the smoothness assumption.展开更多
The solvability of the interpolation by bivariate polynomials based on multivariate F-truncated powers is considered in this short note. It unifies the pointwise Lagrange interpolation by bivariate polynomials and the...The solvability of the interpolation by bivariate polynomials based on multivariate F-truncated powers is considered in this short note. It unifies the pointwise Lagrange interpolation by bivariate polynomials and the interpolation by bivariate polynomials based on linear integrals over segments in some sense.展开更多
文摘The solvability of the fifth-order nonlinear dispersive equation δtu＋au （δxu）^2＋βδx^3u＋γδx^5u = 0 is studied. By using the approach of Kenig, Ponce and Vega and some Strichartz estimates for the corresponding linear problem,it is proved that if the initial function u0 belongs to H^5（R） and s〉1/4,then the Cauchy problem has a unique solution in C（[-T,T],H^5（R）） for some T〉0.
文摘In this paper, we study the initial-boundary value problem with rigid wall for the equations in combustion dynamics with largy parameter. Introducing variable scalar norms and two seminorms, making use of the vorticity operator, overcome the difficulty from the large parameter. By energy estimation, the existence and unique theorems of local smooth solution is proved.
基金Supported in part by National Natural Science Foundation of China under Grant Nos.10605013 and 10975075 the Fundamental Research Funds for the Central Universities
文摘The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods.Furthermore the connection between the model and an anharmonic oscillator is investigated by methods of KStransformation.
基金the Ministry of Education and Science of the Republic of Kazakhstan for a grant
文摘In this work, we present final solving Millennium Prize Problems formulated by Clay Math. Inst., Cambridge. A new uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided. We also describe the loss of smoothness of classical solutions for the Navier-Stokes equations.
基金the Ministry of Education and Science of the Republic of Kazakhstan for a grant
文摘The analytic properties of the scattering amplitude are discussed, and a representation of the potential is obtained using the scattering amplitude. A uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided. The paper also describes the time blowup of classical solutions for the Navier-Stokes equations by the smoothness assumption.
文摘The solvability of the interpolation by bivariate polynomials based on multivariate F-truncated powers is considered in this short note. It unifies the pointwise Lagrange interpolation by bivariate polynomials and the interpolation by bivariate polynomials based on linear integrals over segments in some sense.
