SPDE in Hilbert space with locally monotone coefficients
By Wei Liu, Michael Röckner. 2010
208 citations recorded by the source corpus.
The aim of this paper is to extend the usual framework of SPDE with monotone coecients to include a large class of cases with merely locally monotone coecients. This new framework is conceptually not more involved than the classical one, but includes many more fundamental examples not included previously. Thus our main result can be applied to various types of SPDEs such as stochastic reaction-diusion equations, stochastic Burgers type equation, stochastic 2-D Navier-Stokes equation, stochastic p-Laplace equation and stochastic porous media equation with non-monotone perturbations.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f19208381dc2df786185086bc873e1033cd79b76
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In Computational Theory and Mathematics
- Wei Liu
- Tusheng Zhang
- Michael Röckner
- Wei David Liu
- Shijie Shang
- Benjamin Gess
- Jiahui Zhu
- Zdzisław Brzeźniak
In Control and Systems Engineering
- Wei Liu
- Tusheng Zhang
- Shijie Shang
- Michael Röckner
- Wei David Liu
- Jiahui Zhu
- Benjamin Gess
- Zdzisław Brzeźniak
In Mathematical Physics
- Tusheng Zhang
- Wei David Liu
- Michael Röckner
- Zdzisław Brzeźniak
- Wei Liu
- Shijie Shang
- Jiahui Zhu
- Benjamin Gess
Citations in the corpus
- Well-posedness of stochastic partial differential equations with Lyapunov condition (2013, methodology): “3) then the existence and uniqueness of strong solutions has been recently established in [23] ((H0) can be avoided in this case).”
- Strong solutions for SPDE with locally monotone coefficients driven by L\'{e}vy noise (2011, methodology): “In [36] the authors showed that the local monotonicity method first used by Menaldi and Sritharan [41] for stochastic 2D Navier-Stokes equations (and later used by Sritharan and Sundar [55], Chueshov and Millet [13] for various stochastic equations of hydrodynamics) can be generalized to such an ext”
- Random attractors for a class of stochastic partial differential equations driven by general additive noise (2010, background): “For general results on the existence and uniqueness of variational solutions to SPDE we refer to [23, 28, 38, 40, 43, 51].”
- Well-posedness of stochastic partial differential equations with fully local monotone coefficients (2022, methodology): “In fact, in [53] it is required that ρ(u) + η(v) either only depend on u or only depend on v when the equation is driven by multiplicative noise.”