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Navier-Stokes Equations
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Schiff's base dichloroacetamides having the formula OR2 PARALLEL HCCl2-C-N ANGLE R1 in which R1 is selected from the group consisting of alkenyl, alkyl, alkynyl and alkoxyalkyl; and R2 is selected by selecting R2 from the groups consisting of lower alkylimino, cyclohexenyl-1 and lower alkynyl substituted cycloenenyl -1 as discussed by the authors.Citations
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Pointwise Error Estimates for Finite Element Solutions of the Stokes Problem
TL;DR: The new pointwise error estimates exhibit a more local dependence of the errors on the true solution and as a by-product provide logarithm-free bounds for all errors except the error of the velocity approximation of the lowest order.
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On Recent Progress for the Stochastic Navier Stokes Equations
TL;DR: In this article, an overview of the ideas central to some recent developments in the ergodic theory of the stochastically forced Navier Stokes equations and other dissipative stochastic partial differential equations is given.
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On a Linearized Backward Euler Method for the Equations of Motion of Oldroyd Fluids of Order One
TL;DR: A linearized backward Euler method is discussed for the equations of motion arising in the Oldroyd model of viscoelastic fluids and some new a priori bounds are obtained for the solution under realistically assumed conditions on the data.
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Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise
TL;DR: In this article, the authors prove the local existence and uniqueness of solutions for a class of stochastic fractional partial differential equations driven by multiplicative noise, and show that adding linear multiplicative noises provides a regularizing effect: the solutions will not blow up with high probability if the initial data is sufficiently small, or if the noise coefficient is sufficiently large.
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Accuracy and stability of filters for dissipative PDEs
TL;DR: Results are described showing that, in the small observational noise limit, the filters can be tuned to perform accurately in tracking the signal itself (filter accuracy), provided the system is observed in a sufficiently large low dimensional space; roughly speaking this space should be large enough to contain the unstable modes of the linearized dynamics.