Local and global well-posedness of SPDE with generalized coercivity conditions

Liu W, Röckner M (2013)
Journal Of Differential Equations 254(2): 725-755.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
In this paper we establish the local and global existence and uniqueness of solutions for general nonlinear evolution equations with coefficients satisfying some local monotonicity and generalized coercivity conditions. An analogous result is obtained for stochastic evolution equations in Hilbert space with additive noise. As applications, the main results are applied to obtain simpler proofs in known cases as the stochastic 3D Navier-Stokes equation, the tamed 3D Navier-Stokes equation and the Cahn-Hilliard equation, but also to get new results for stochastic surface growth PDE and stochastic power law fluids. (C) 2012 Elsevier Inc. All rights reserved.
Stichworte
Cahn-Hilliard equation; Surface growth model; Navier-Stokes equation; Local monotonicity; Generalized coercivity; Power law fluid
Erscheinungsjahr
2013
Zeitschriftentitel
Journal Of Differential Equations
Band
254
Ausgabe
2
Seite(n)
725-755
ISSN
0022-0396
Page URI
https://pub.uni-bielefeld.de/record/2548347

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Liu W, Röckner M. Local and global well-posedness of SPDE with generalized coercivity conditions. Journal Of Differential Equations. 2013;254(2):725-755.
Liu, W., & Röckner, M. (2013). Local and global well-posedness of SPDE with generalized coercivity conditions. Journal Of Differential Equations, 254(2), 725-755. doi:10.1016/j.jde.2012.09.014
Liu, W., and Röckner, M. (2013). Local and global well-posedness of SPDE with generalized coercivity conditions. Journal Of Differential Equations 254, 725-755.
Liu, W., & Röckner, M., 2013. Local and global well-posedness of SPDE with generalized coercivity conditions. Journal Of Differential Equations, 254(2), p 725-755.
W. Liu and M. Röckner, “Local and global well-posedness of SPDE with generalized coercivity conditions”, Journal Of Differential Equations, vol. 254, 2013, pp. 725-755.
Liu, W., Röckner, M.: Local and global well-posedness of SPDE with generalized coercivity conditions. Journal Of Differential Equations. 254, 725-755 (2013).
Liu, Wei, and Röckner, Michael. “Local and global well-posedness of SPDE with generalized coercivity conditions”. Journal Of Differential Equations 254.2 (2013): 725-755.