On infinite energy solutions to dissipative PDEs in unbounded domains.
Pennant, Jonathan P. (2016) On infinite energy solutions to dissipative PDEs in unbounded domains. Doctoral thesis, University of Surrey.
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In this thesis several problems in Partial Differential Equations in unbounded domains are studied using the techniques of uniformly local spaces and weighted energy theory. First Coupled Burger's equations are studied on the whole space R and existence of solutions in uniformly local spaces is proven in the case where the non-linearity is gradient. Moreover the uniqueness of these solutions and some additional regularity is proven. Second the Cahn-Hilliard, and closely related Cahn-Hilliard-Oono, equations are studied on the whole space R3 with both polynomial and singular potentials and existence of solutions in uniformly local spaces is proven. Moreover uniqueness and additional regularity of these equations is also proven. Third the Navier-Stokes equations are studied on the whole space R2 and, building on the work of Zelik who showed the existence of solutions in uniformly local spaces, the existence of a finite dimensional globally compact attractor is proven in the case where the forcing term has arbitrarily slow decay at infinity.
|Item Type:||Thesis (Doctoral)|
|Subjects :||Mathematics, Partial Differential Equations|
|Date :||30 June 2016|
|Depositing User :||Jonathan Pennant|
|Date Deposited :||12 Jul 2016 08:05|
|Last Modified :||12 Jul 2016 08:05|
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