Local and global well-posedness of SPDE with generalized coercivity conditions☆
By Wei Liu, Michael Röckner. 2012
119 citations recorded by the source corpus.
Abstract 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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/87304d6af6a138b71c515504088332b89341cfe1
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In Applied Mathematics
- Wei Liu
- Michael Röckner
- Tusheng Zhang
- Shijie Shang
- Wei David Liu
- Zdzisław Brzeźniak
- Jiahui Zhu
- Xicheng Zhang
In Mathematical Physics
- Tusheng Zhang
- Wei David Liu
- Michael Röckner
- Zdzisław Brzeźniak
- Wei Liu
- Shijie Shang
- Jiahui Zhu
- Xicheng Zhang
Citations in the corpus
- Well-posedness of stochastic partial differential equations with Lyapunov condition (2013, background): “Another remark is that in [22](see also [24]) we introduced a more general type of local monotonicity condition (see (3.”
- Strong solutions for SPDE with locally monotone coefficients driven by L\'{e}vy noise (2011, methodology): “n approximation and showed the tightness of the distributions of the corresponding approximating solutions. Then they proved that the limit is a weak solution of (4.22) with additive Wiener noise. In [37] the authors obtained the existence and uniqueness of strong solutions for (4.22) with multiplic”
- Well-posedness of stochastic partial differential equations with fully local monotone coefficients (2022, methodology): “We refer the reader to [23, 17, 54, 2, 22] and reference therein.”