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Title: A few problems on stochastic geometric wave equations
Author: Rana, Nimit
ISNI:       0000 0004 8499 1541
Awarding Body: University of York
Current Institution: University of York
Date of Award: 2019
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In this thesis, we study three problems on stochastic geometric wave equations. First, we prove the existence of a unique local maximal solution to an energy critical stochastic wave equation with multiplicative noise on a smooth bounded domain D ⊂ R² with exponential nonlinearity. The main ingredients in the proof are appropriate deterministic and stochastic Strichartz inequalities which are derived in suitable spaces. In the second part, we verify a large deviation principle for the small noise asymptotic of strong solutions to stochastic geometric wave equations. The method of proof relies on applying the weak convergence approach of Budhiraja and Dupuis to SPDEs where solutions are local Sobolev spaces valued stochastic processes. The final result contained in this thesis concerns the local well-posedness theory for geometric wave equations, perturbed by a fractional Gaussian noise, on one dimensional Minkowski space R¹⁺¹ when the target manifold M is a compact Riemannian manifold and the initial data is rough. Here, to achieve the existence and the uniqueness of a local solution we extend the theory of pathwise stochastic integrals in Besov spaces to two dimensional case.
Supervisor: Brzezniak, Zdzislaw Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available