The initial value problem for the generalized Korteweg-deVries equation of order three on the line is shown to be globally well posed for rough data. Our proof is based on the multilinear estimate and the I-method int...The initial value problem for the generalized Korteweg-deVries equation of order three on the line is shown to be globally well posed for rough data. Our proof is based on the multilinear estimate and the I-method introduced by Colliander, Keel, Staffilani, Takaoka, and Tao.展开更多
Let G be a non-empty closed (resp. bounded closed) boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X. Let denote the space of all non-empty compact convex subsets of X endowed with ...Let G be a non-empty closed (resp. bounded closed) boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X. Let denote the space of all non-empty compact convex subsets of X endowed with the Hausdorff distance. Moreover, let denote the closure of the set . We prove that the set of all , such that the minimization (resp. maximization) problem min(A,G) (resp. max(A,G)) is well posed, contains a dense G δ-subset of , thus extending the recent results due to Blasi, Myjak and Papini and Li.展开更多
This paper studies first order semilinear hyperbolic systems in n(n≥2)space dimensions.Under the hypothesis that the system satisfies so called`null condition',the local well posedness for its Cauchy problem with...This paper studies first order semilinear hyperbolic systems in n(n≥2)space dimensions.Under the hypothesis that the system satisfies so called`null condition',the local well posedness for its Cauchy problem with initial data in H n-12 is proved.展开更多
文摘The initial value problem for the generalized Korteweg-deVries equation of order three on the line is shown to be globally well posed for rough data. Our proof is based on the multilinear estimate and the I-method introduced by Colliander, Keel, Staffilani, Takaoka, and Tao.
基金partly supported by the National Natural Science Foundation of China(Grant No,10271025)
文摘Let G be a non-empty closed (resp. bounded closed) boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X. Let denote the space of all non-empty compact convex subsets of X endowed with the Hausdorff distance. Moreover, let denote the closure of the set . We prove that the set of all , such that the minimization (resp. maximization) problem min(A,G) (resp. max(A,G)) is well posed, contains a dense G δ-subset of , thus extending the recent results due to Blasi, Myjak and Papini and Li.
文摘This paper studies first order semilinear hyperbolic systems in n(n≥2)space dimensions.Under the hypothesis that the system satisfies so called`null condition',the local well posedness for its Cauchy problem with initial data in H n-12 is proved.
