A Non-autonomous Incompressible Non-Newtonian Fluid In Locally Uniform Spaces

In this master's dissertation,we mainly consider the existence and uniqueness of solutions and pullback attractors in the setting of locally uniform spaces for a non-autonomous incompressible non-Newtonian fluid in the two-dimensional unbounded domain.We know that in contrary to the case of a bounded domain,in an unbounded domain,the family of spaces L~p are not nested,typical Sobelev embeddings are not compact and the constant functions are not integrable any longer.These drawbacks make the problem in unbounded domains much more involved.So,in some sense, locally uniform spaces turn out to be very nature and useful.Since they enjoy suitable nesting properties,constant functions lie within them and they have locally compact embeddings,the general Lebesgue integrable function spaces and Sobolev spaces are all the subspaces of corresponding locally uniform spaces.So when we choose locally uniform spaces as the space setting for our problem,we can not only make our analysis much more simple,but also allow more general initial data to get large classes of solutions.For convenience,we first introduce the definition and some properties of locally uniform spaces;then,we give the result of existence and uniqueness of solutions to a non-autonomous incompressible non-Newtonian fluid in locally uniform spaces;lastly,we discuss the existence of pullback attractors for the system.