The aim of this paper is to clarify the role played by resolvent estimates for nonlinear stability.We will give examples showing that a large resolvent may lead to a small domain of nonlinear stability.In other exampl...The aim of this paper is to clarify the role played by resolvent estimates for nonlinear stability.We will give examples showing that a large resolvent may lead to a small domain of nonlinear stability.In other examples the resolvent is large,but the domain of nonlinear stability is completely unrestricted.Which case prevails depends on the details of the problem. We will also show that the size of the resolvent depends in an essential way on the norms that are used.展开更多
基金Supported by Office of Naval Research n00014 90 j 1382Supported by NSF Grant DMS-9404124 and DOE Grant DE-FG03-95ER25235
文摘The aim of this paper is to clarify the role played by resolvent estimates for nonlinear stability.We will give examples showing that a large resolvent may lead to a small domain of nonlinear stability.In other examples the resolvent is large,but the domain of nonlinear stability is completely unrestricted.Which case prevails depends on the details of the problem. We will also show that the size of the resolvent depends in an essential way on the norms that are used.
