English

Stochastic hydrodynamic-type evolution equations driven by L\'{e}vy noise in 3D unbounded domains - abstract framework and applications

Probability 2013-06-25 v1

Abstract

The existence of martingale solutions of the hydrodynamic-type equations in 3D possibly unbounded domains is proved. The construction of the solution is based on the Faedo-Galerkin approximation. To overcome the difficulty related to the lack of the compactness of Sobolev embeddings in the case of unbounded domain we use certain Fr\'{e}chet space. We use also compactness and tightness criteria in some nonmetrizable spaces and a version of the Skorokhod Theorem in non-metric spaces. The general framework is applied to the stochastic Navier-Stokes, magneto-hydrodynamic (MHD) and the Boussinesq equations.

Keywords

Cite

@article{arxiv.1306.5342,
  title  = {Stochastic hydrodynamic-type evolution equations driven by L\'{e}vy noise in 3D unbounded domains - abstract framework and applications},
  author = {Elżbieta Motyl},
  journal= {arXiv preprint arXiv:1306.5342},
  year   = {2013}
}

Comments

arXiv admin note: text overlap with arXiv:1112.5570

R2 v1 2026-06-22T00:38:36.010Z