Lower Bounds Of The Blowup Rate For A Type Of Generalized Zakharov System

In this thesis,we study the lower bound for the blowup rate of fininte time blowup solutions for a type of generalized Zakharov system in two spa-tial dimensions（?）The system describes the self generated effect of magnetic field in a cold plasma under the case that the ratio of the plasma frequency and the ion ve-locity tends to zero.The system consists of a nonlinear Schr（?）dinger equation and a wave equation with a second-order derivative nonlinearity.Compared with the classical Zakharov sustem,this system involves two extra terms E₂（E₁（?）-（?）E₂）and E₁（（?）E₂-E₁（?））which are generated by the nonlo-cal effect（the effect of magnetic field）,which makes it difficult to estimate the lower bound of the blowup rate for finite time blow-up solutions to the system under consideration.This paper is composed of four parts.The first part introduces the re-search background as well as the current situation and development trend at home and abroad for the classical and the magnetic Zakharov system.In the second part,we mention some preliminaries:the theory of Sobolev s-paces,Gronwall inequality,interpolation inequalities and the theory on op-erator semigroup,for preparing for the quantitative and quanlitative analysis of solutions to the system（B-Z）.In the third part,we prove the main result with the given components in the second part.We first derive the conser-vation laws of the mass and of the energy for the System（B-Z）,study the well-posedness of its solutions,and establish a re-scaled system with the aid of scaling with respect to space and time.Next,we consider the glob-al existence of smooth solutions for the re-scaled system.Furthermore,we derive a lower bound of blow-up rate of the finite time blow-up solutions（E₁,E₂,n,v）（t）to the System（B-Z）,that is,when t→T（T the finite blow-up time）,there exists a c>0 depending only on initial data（E₁0,E₂0,n₀,v₀）such that‖（E₁,E₂,n,v）‖H¹（R²）×H¹（R²）×L²（R²）×L²（R²）≥（?）Finally,in the fourth part,we mainly summarize some unsolved problems related in the present thesis.