Up to now,the most widely used method for transition prediction is the one based on linear stability theory.When it is applied to three-dimensional boundary layers,one has to choose the direction,or path,along which t...Up to now,the most widely used method for transition prediction is the one based on linear stability theory.When it is applied to three-dimensional boundary layers,one has to choose the direction,or path,along which the growth rate of the disturbance is to be integrated.The direction given by using saddle point method in the theory of complex variable function is seen as mathematically most reasonable.However,unlike the saddle point method applied to water waves,here its physical meaning is not so obvious,as the frequency and wave number may be complex.And on some occasions,in advancing the integration of the growth rate of the disturbance,up to a certain location,one may not be able to continue the integration,because the condition for specifying the direction set by the saddle point method can no longer be satisfied on the basis of continuously varying wave number.In this paper,these two problems are discussed,and suggestions for how to do transition prediction under the latter condition are provided.展开更多
This paper introduces a generic eigenvalue flow of a parameter family of operators, where the corresponding eigenfunction is continuous in parameters. Then the author applies the result to the study of polynomial grow...This paper introduces a generic eigenvalue flow of a parameter family of operators, where the corresponding eigenfunction is continuous in parameters. Then the author applies the result to the study of polynomial growth L-harmonic functions. Under the assumption that the operator has some weakly conic structures at infinity which is not necessarily unique, a Harnack type uniform growth estimate is obtained.展开更多
We consider the quasilinear Schrdinger equations of the form-ε~2？u ＋ V（x）u- ε~2？（u2）u = g（u）, x ∈ R^N,where ε 〉 0 is a small parameter, the nonlinearity g（u） ∈ C^1（R） is an odd function with subcrit...We consider the quasilinear Schrdinger equations of the form-ε~2？u ＋ V（x）u- ε~2？（u2）u = g（u）, x ∈ R^N,where ε 〉 0 is a small parameter, the nonlinearity g（u） ∈ C^1（R） is an odd function with subcritical growth and V（x） is a positive Hlder continuous function which is bounded from below, away from zero, and infΛV（x） 0 such that for all ε∈（0, ε0],the above mentioned problem possesses a sign-changing solution uε which exhibits concentration profile around the local minimum point of V（x） as ε→ 0~＋.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 11002098 and 11332007)
文摘Up to now,the most widely used method for transition prediction is the one based on linear stability theory.When it is applied to three-dimensional boundary layers,one has to choose the direction,or path,along which the growth rate of the disturbance is to be integrated.The direction given by using saddle point method in the theory of complex variable function is seen as mathematically most reasonable.However,unlike the saddle point method applied to water waves,here its physical meaning is not so obvious,as the frequency and wave number may be complex.And on some occasions,in advancing the integration of the growth rate of the disturbance,up to a certain location,one may not be able to continue the integration,because the condition for specifying the direction set by the saddle point method can no longer be satisfied on the basis of continuously varying wave number.In this paper,these two problems are discussed,and suggestions for how to do transition prediction under the latter condition are provided.
文摘This paper introduces a generic eigenvalue flow of a parameter family of operators, where the corresponding eigenfunction is continuous in parameters. Then the author applies the result to the study of polynomial growth L-harmonic functions. Under the assumption that the operator has some weakly conic structures at infinity which is not necessarily unique, a Harnack type uniform growth estimate is obtained.
基金supported by National Natural Science Foundation of China(Grant Nos.11371160 and 11328101)the Program for Changjiang Scholars and Innovative Research Team in University(Grant No.#IRT13066)
文摘We consider the quasilinear Schrdinger equations of the form-ε~2？u ＋ V（x）u- ε~2？（u2）u = g（u）, x ∈ R^N,where ε 〉 0 is a small parameter, the nonlinearity g（u） ∈ C^1（R） is an odd function with subcritical growth and V（x） is a positive Hlder continuous function which is bounded from below, away from zero, and infΛV（x） 0 such that for all ε∈（0, ε0],the above mentioned problem possesses a sign-changing solution uε which exhibits concentration profile around the local minimum point of V（x） as ε→ 0~＋.
