Stochastic generalized magnetohydrodynamics equations: well-posedness

References

• Fan J , Malaikah H , Monaquel S , et al . Global Cauchy problem of 2D generalized MHD equations. Monatsh Math. 2014;175(1):127–131.
   Web of Science ®Google Scholar
• Huang J , Shen T . Well-posedness and dynamics of the stochastic fractional magneto-hydrodynamic equations. Nonlinear Anal. 2016;133:102–133.
   Web of Science ®Google Scholar
• Wu J . Generalized MHD equations. J Differ Equ. 2003;195(2):284–312.
   Web of Science ®Google Scholar
• Wu J . Regularity criteria for the generalized MHD equations. Commun Partial Differ Equ. 2003;33(1–3):285–306.
   Google Scholar
• Wu G . Regularity criteria for the 3D generalized MHD equations in terms of vorticity. Nonlinear Anal. 2009;71(9):4251–4258.
   Web of Science ®Google Scholar
• Yuan J . Existence theorem and regularity criteria for the generalized MHD equations. Nonlinear Anal Real World Appl. 2010;11(3):1640–1649.
   Web of Science ®Google Scholar
• Barbu V , Da Prator G . Existence and ergodicity for the two-dimensional stochastic magneto-hydrodynamics equations. Appl Math Optim. 2007;56(2):145–168.
   Web of Science ®Google Scholar
• Chueshov I , Millet A . Stochastic 2D hydrodynamical type systems: well posedness and large deviations. Appl Math Optim. 2010;61(3):379–420.
   Web of Science ®Google Scholar
• Motyl E . Stochastic hydrodynamic-type evolution equations driven by Lévy noise in 3D unbounded domains -– abstract framework and applications. Stoch Process Appl. 2014;124(6):2052–2097.
   Web of Science ®Google Scholar
• Sango M . Magnetohydrodynamic turbulent flows: existence results. Phys D. 2010;239(12):912–923.
   Web of Science ®Google Scholar
• Sango M , Tegegn TA . Harmonic analysis tools for stochastic magnetohydrodynamics equations in Besov spaces. Internat J Modern Phys B. 2016;30(28–29):1640025, 13.
   Web of Science ®Google Scholar
• Sritharan SS , Sundar P . The stochastic magneto-hydrodynamic system. Infin Dimens Anal Quantum Probab Relat Top. 1999;2(2):241–265.
   Web of Science ®Google Scholar
• Sundar P . Stochastic magneto-hydrodynamic system perturbed by general noise. Commun Stoch Anal. 2010;4(2):253–269.
   Google Scholar
• Yamazaki K . Stochastic Hall-magneto-hydrodynamics system in three and two and a half dimensions. J Stat Phys. 2017;166(2):368–397.
   Web of Science ®Google Scholar
• Yamazaki K . Exponential convergence of the stochastic micropolar and magneto-micropolar fluid systems. Commun Stoch Anal. 2016;10(3):271–295.
   Google Scholar
• Yamazaki K . 3-D stochastic micropolar and magneto-micropolar fluid systems with non-Lipschitz multiplicative noise. Commun Stoch Anal. 2014;8(3):413–437.
   Google Scholar
• Jakubowski A . The almost sure Skorokhod representation for subsequences in nonmetric spaces. Teor Veroyatnost Primenen. 1997;42(1):209–216 (English, with Russian summary): English transl., Theory Probab Appl. 42(1):167--174 (1997), 1998.
   Web of Science ®Google Scholar
• Brzeźniak Z , Motyl E . Existence of a martingale solution of the stochastic Navier-Stokes equations in unbounded 2D and 3D domains. J Differ Equ. 2013 Feb;254(4):1627–1685.
   Web of Science ®Google Scholar
• Brzeźniak Z , Ferrario B . A note on stochastic Navier-Stokes equations with not regular multiplicative noise. Stoch Partial Differ Equ Anal Comput. 2017;5(1):53–80.
   Web of Science ®Google Scholar
• Brzeźniak Z , Ferrario B . Stationary solutions for stochastic damped Navier-Stokes equations in ℛd . Indiana Univ Math J. 2017 Apr 30.
   Web of Science ®Google Scholar
• Flandoli F , Gatarek D . Martingale and stationary solutions for stochastic Navier-Stokes equations. Probab Theory Related Fields. 1995;102(3):367–391.
   Web of Science ®Google Scholar
• Bergh J , Löfström J . Interpolation spaces. An introduction. Vol. 223, Grundlehren der Mathematischen Wissenschaften. Berlin: Springer-Verlag; 1976. MR0482275.
   Google Scholar
• Holly K , Wiciak M . Compactness method applied to an abstract nonlinear parabolic equation, Selected problems of mathematics. In: 50th Anniversary Cracow University of Technology. Anniversary Issue, 6. Kraków: Cracow University of Technology; 1995. p. 95–160.
   Google Scholar
• Temam R . Navier-Stokes equations. Theory and numerical analysis. Vol. 2, Studies in Mathematics and its Applications. Amsterdam: North-Holland; 1977.
   Google Scholar
• Da Prato G , Zabczyk J . Stochastic equations in infinite dimensions. 2nd ed. Vol. 152, Encyclopedia of Mathematics and its Applications. Cambridge: Cambridge University Press; 2014.
   Google Scholar
• Mihlin SG . On the multipliers of Fourier integrals. Dokl Akad Nauk SSSR (N S). 1956;109:701–703. Russian.
   Google Scholar
• Reed M , Simon B . Methods of modern mathematical physics. I. Functional analysis. New York (NY): Academic Press; 1972.
   Google Scholar
• Skorohod AV . Studies in the theory of random processes. Reading (MA): Addison-Wesley; 1965, 199 (Translated from the Russian by Scripta Technica, Inc.).
   Google Scholar
• Albeverio S , Brzeźniak Z , Wu J-L . Existence of global solutions and invariant measures for stochastic differential equations driven by Poisson type noise with non-Lipschitz coefficients. J Math Anal Appl. 2010;371(1):309–322.
   Web of Science ®Google Scholar
• Duan J , Millet A . Large deviations for the Boussinesq equations under random influences. Stoch Process Appl. 2009;119(6):2052–2081.
   Web of Science ®Google Scholar