A necessary and sufficient conditions of the existence of formal solution to the initial value problem of Navier-Stokes equation an R-3 x R are presented. A computation case is also given.
Based on stratification theory, the existence theorems of formal solutions of partial differential equation (PDE) are given . And the relationship between formal solutions and protective limit of Ehresmann chain is pr...Based on stratification theory, the existence theorems of formal solutions of partial differential equation (PDE) are given . And the relationship between formal solutions and protective limit of Ehresmann chain is presented .展开更多
We study the exact formal solution to the simplified Keller-Segel system modelling chemotaxis. The method we use is series expanding. The main result is to attain the formal solution to the simplified Keller-Segel sys...We study the exact formal solution to the simplified Keller-Segel system modelling chemotaxis. The method we use is series expanding. The main result is to attain the formal solution to the simplified Keller-Segel system.展开更多
In this paper the authors consider the summability of formal solutions for some first order singular PDEs with irregular singularity. They prove that in this case the formal solutions will be divergent, but except a e...In this paper the authors consider the summability of formal solutions for some first order singular PDEs with irregular singularity. They prove that in this case the formal solutions will be divergent, but except a enumerable directions, the formal solutions are Borel summable.展开更多
It is proved that the ill-posed initial value problem of the Euler equations for compressible adiabatic inviscid fluid flow can be only formally solved. The necessary and sufficient conditions for existence of formal ...It is proved that the ill-posed initial value problem of the Euler equations for compressible adiabatic inviscid fluid flow can be only formally solved. The necessary and sufficient conditions for existence of formal solution of some representative ill-posedness initial-boundary value problem are presented. Finally, an example is also given.展开更多
In this article, we study on the existence of solution for a singularities of a system of nonlinear fractional differential equations （FDE）. We construct a formal power series solution for our considering FDE and pr...In this article, we study on the existence of solution for a singularities of a system of nonlinear fractional differential equations （FDE）. We construct a formal power series solution for our considering FDE and prove convergence of formal so- lutions under conditions. -We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function.展开更多
The solvability of the Euler equations about incompressible inviscid fluid based on the stratification theory is discussed. And the conditions for the existence of formal solutions and the methods are presented for ca...The solvability of the Euler equations about incompressible inviscid fluid based on the stratification theory is discussed. And the conditions for the existence of formal solutions and the methods are presented for calculating all kinds of ill-posed initial value problems. Two examples are given as the evidences that the initial problems at the hyper surface does not exist any unique solution.展开更多
文摘A necessary and sufficient conditions of the existence of formal solution to the initial value problem of Navier-Stokes equation an R-3 x R are presented. A computation case is also given.
基金the National Natural Science Foundation of China( 19971054,40175014)
文摘Based on stratification theory, the existence theorems of formal solutions of partial differential equation (PDE) are given . And the relationship between formal solutions and protective limit of Ehresmann chain is presented .
文摘We study the exact formal solution to the simplified Keller-Segel system modelling chemotaxis. The method we use is series expanding. The main result is to attain the formal solution to the simplified Keller-Segel system.
基金supported by the NSFC and the 973 key project of the MOST
文摘In this paper the authors consider the summability of formal solutions for some first order singular PDEs with irregular singularity. They prove that in this case the formal solutions will be divergent, but except a enumerable directions, the formal solutions are Borel summable.
基金Project supported by the National Natural Science Foundation of China （Major Program of the Tenth Five-Year Plan） （Grant No,90411006）
文摘It is proved that the ill-posed initial value problem of the Euler equations for compressible adiabatic inviscid fluid flow can be only formally solved. The necessary and sufficient conditions for existence of formal solution of some representative ill-posedness initial-boundary value problem are presented. Finally, an example is also given.
文摘In this article, we study on the existence of solution for a singularities of a system of nonlinear fractional differential equations （FDE）. We construct a formal power series solution for our considering FDE and prove convergence of formal so- lutions under conditions. -We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function.
文摘The solvability of the Euler equations about incompressible inviscid fluid based on the stratification theory is discussed. And the conditions for the existence of formal solutions and the methods are presented for calculating all kinds of ill-posed initial value problems. Two examples are given as the evidences that the initial problems at the hyper surface does not exist any unique solution.
