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The Global Attractor of the Generalized Viscous Damped Forced Ostrovsky Equation

Author: GaoAnNa
Tutor: TianLiXin
School: Jiangsu University
Course: Applied Mathematics
Keywords: Global attractor Ostrovsky equation Fourier restriction operators Bourgain function space energy equation method Splitting of the solution
CLC: O175.29
Type: Master's thesis
Year: 2008
Downloads: 28
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Abstract


In the paper,the existence of the global attractor of the Ostrovsky equation is considered by the Fourier restriction norm method,the energy equation method and the conjunction with a suitable splitting of the solutions.It is important to point out that the phase functions,their first-order derivatives and second-order derivatives have non-aero singular points,which makes the problem much more difficult. However;we can overcome the difficulties by the Fourier restriction operators to separate these singular points.The dissertation consists of four chanters.In Chapter 1,we introduce the background and summarize of the global attractor and Ostrovsky equation.In Chapter 2,we introduce the basic concept of flood wave equations and the global attractor.At the same time,we sum up some methods about the study of global attractor.In Chapter 3,the existence of the global attractor of the viscous damped forced Ostrovsky equation is considered.First,we introduce the definition of the modified Bourgain function space and its qualities which include norm and the trivial embedding relation.Then we use some linear estimates and bilinear estimates to study the Cauchy problems of the equation.Next we obtain the existence of the global attractor in(?)~2(R)and its boundedness in(?)~s(R)by the energy equation method together with a splitting of the solution.Finally we show that the global attractor is compact of in(?)~s(R).In Chapter 4,the existence of the global attractor of the generalized viscous damped forced Ostrovsky equation is studied.Applying Bourgain function space, energy equation method together with multi-linear,we obtain that the equation possesses the global attractor in(?)~2(R) and the solution is regular in(?)~s(R).

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations > Nonlinear partial differential equations
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