Given two left Oc-analytic functions f, g in some open set Ω of R8, we obtain some sufficient conditions for fg is also left Oc-analytic in Ω. Moreover, we prove?fλ that is a left Oc-analytic function for any const...Given two left Oc-analytic functions f, g in some open set Ω of R8, we obtain some sufficient conditions for fg is also left Oc-analytic in Ω. Moreover, we prove?fλ that is a left Oc-analytic function for any constants λ∈Oc if and only if is a complex Stein-Weiss conjugate harmonic system. Some applications and connections with Cauchy-Kowalewski product are also considered.展开更多
We study 2D and 3D Prandtl equations of degenerate hyperbolic type,and establish without any structural assumption the Gevrey well-posedness with Gevrey index≤2.Compared with the classical parabolic Prandtl equations...We study 2D and 3D Prandtl equations of degenerate hyperbolic type,and establish without any structural assumption the Gevrey well-posedness with Gevrey index≤2.Compared with the classical parabolic Prandtl equations,the loss of the derivatives,caused by the hyperbolic feature coupled with the degeneracy,cannot be overcame by virtue of the classical cancellation mechanism that developed for the parabolic counterpart.Inspired by the abstract Cauchy-Kowalewski theorem and by virtue of the hyperbolic feature,we give in this text a straightforward proof,basing on an elementary L^(2)energy estimate.In particular our argument does not involve the cancellation mechanism used efficiently for the classical Prandtl equations.展开更多
文摘Given two left Oc-analytic functions f, g in some open set Ω of R8, we obtain some sufficient conditions for fg is also left Oc-analytic in Ω. Moreover, we prove?fλ that is a left Oc-analytic function for any constants λ∈Oc if and only if is a complex Stein-Weiss conjugate harmonic system. Some applications and connections with Cauchy-Kowalewski product are also considered.
基金supported by the NSF of China(Grant Nos.11961160716,11871054,12131017)the Natural Science Foundation of Hubei Province(Grant No.2019CFA007).
文摘We study 2D and 3D Prandtl equations of degenerate hyperbolic type,and establish without any structural assumption the Gevrey well-posedness with Gevrey index≤2.Compared with the classical parabolic Prandtl equations,the loss of the derivatives,caused by the hyperbolic feature coupled with the degeneracy,cannot be overcame by virtue of the classical cancellation mechanism that developed for the parabolic counterpart.Inspired by the abstract Cauchy-Kowalewski theorem and by virtue of the hyperbolic feature,we give in this text a straightforward proof,basing on an elementary L^(2)energy estimate.In particular our argument does not involve the cancellation mechanism used efficiently for the classical Prandtl equations.
