Some mathematical questions related to the mhd equations

Sermange, Michel; Témam, Roger

doi:10.1002/cpa.3160360506

Cited by 927 publications

(327 citation statements)

References 11 publications

Supporting

Mentioning

319

Contrasting

Unclassified

Order By: Relevance

“…As the basis functions, we can take the eigenfunctions of the Laplacian equipped with the Navier boundary conditions (cf. Sections 2.3 and 3.2 in [6] and Section 3 in [23]). …”

Section: Zampmentioning

confidence: 99%

“…The crucial point is that (1.10) is constructed through revolving Ω ϕ0 around x 3 -axis [see (1.6)], thus any solution to 2d problem in a bounded, smooth domain (for such solutions see e.g. [5,6]), which is separated from the axis of rotation, would be a good candidate for a special solution (v s , H s ). This idea seems to work for even more general MHD models (fractional diffusion, partial diffusion, etc.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On global regular solutions to magnetohydrodynamics in axi-symmetric domains

Nowakowski

Zaja̧czkowski

2016

Z. Angew. Math. Phys.

View full text Add to dashboard Cite

Abstract.We consider mhd equations in three-dimensional axially symmetric domains under the Navier boundary conditions for both velocity and magnetic fields. We prove the existence of global, regular axi-symmetric solutions and examine their stability in the class of general solutions to the mhd system. As a consequence, we show the existence of global, regular solutions to the mhd system which are close in suitable norms to axi-symmetric solutions.Mathematics Subject Classification. 35Q35, 76D03, 76W05.

show abstract

“…As the basis functions, we can take the eigenfunctions of the Laplacian equipped with the Navier boundary conditions (cf. Sections 2.3 and 3.2 in [6] and Section 3 in [23]). …”

Section: Zampmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On global regular solutions to magnetohydrodynamics in axi-symmetric domains

Nowakowski

Zaja̧czkowski

2016

Z. Angew. Math. Phys.

View full text Add to dashboard Cite

show abstract

“…V 0 , H 0 and V 0 defined by (6.4), (6.5), (6.6) and spaces used in the theory of the Maxwell equations (spaces denoted with the subscript 1). Namely, see [44],…”

Section: Magneto-hydrodynamic Equations (Mhd)mentioning

confidence: 99%

“…Using the form b defined by (6.10) we will consider the tri-linear formb on V × V × V, where V is defined by (6.33), see Sango [43] and Sermange and Temam [44]. Namely,b…”

Section: Magneto-hydrodynamic Equations (Mhd)mentioning

confidence: 99%

Stochastic hydrodynamic-type evolution equations driven by Lévy noise in 3D unbounded domains—Abstract framework and applications

Motyl

2014

Stochastic Processes and their Applications

View full text Add to dashboard Cite

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 Fréchet 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.

show abstract

“…See [88] for a statement of the wellposedness of MHD equations in bounded domains. However, there are no results about the well-posedness of 3D MHD equations in unbounded domain; such a study is beyond the scope of this book.…”

Section: Remark 62mentioning

confidence: 99%