The Well-posedness Of Global Solutions For Fourth Order Equations In Minus Index Sobolev Space

The initial value problems for a Boussinesq equation and a Euler-Bernoulli equation are established in the following Sobolev spaceFirstly, in this minus index Sobolev space, we prove the Sobolev multiplying lemma by using microlocal analysis. The well-posedness of global solutions is obtained for the following Boussinesq equationIn the mean time, we gain the formula of long time asymptotics for the problem discussed in this chapter.In chaptert 3, the well-posedness of global solutions of Cauchy problem for the following Euler-Bernoulli Beam equationis present under some assumptions on the initial data and nonlinear term f(u) in the minus index Sobolev space.As for as the author knows, the well-posedness of the global solution to the nonlinear problem defined in this paper has not been established before in the minus index Sobolev space...