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Stochastic quasilinear evolution equations in UMD Banach spaces
Author(s) -
Mohan Manil T.,
Sritharan Sivaguru S.
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600015
Subject(s) - mathematics , uniqueness , banach space , class (philosophy) , cover (algebra) , nonlinear system , stochastic differential equation , stopping time , mathematical analysis , pure mathematics , stochastic partial differential equation , partial differential equation , statistics , computer science , mechanical engineering , physics , quantum mechanics , artificial intelligence , engineering
In this work we prove the existence and uniqueness up to a stopping time for the stochastic counterpart of Tosio Kato's quasilinear evolutions in UMD Banach spaces. These class of evolutions are known to cover a large class of physically important nonlinear partial differential equations. Existence of a unique maximal solution as well as an estimate on the probability of positivity of stopping time is obtained. An example of stochastic Euler and Navier–Stokes equation is also given as an application of abstract theory to concrete models.