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Regularity Criteria for the Energy Equality to the 3D Magneto-Hydrodynamics Equations

  • Author / Creator
    Pineau, Mark
  • We consider the Cauchy problem to the Magneto-Hydrodynamics Equations (MHD) in R^3, and present specific criteria for which its corresponding energy equality holds. Specifically, we show that very weak solutions to the MHD equations (in the distributional sense) satisfy the energy equality, provided they belong to the space L^r(0, T; L^s(R^3)) with 2/r+2/s = 1 for s ≥ 4. Further, we also consider
    regularity criteria on the gradient of the solution to the MHD Cauchy problem. That is, we show very weak solutions to the MHD equations satisfy the energy equality if ∇u, ∇B ∈ L^(8s/(9s−12)) (0, T; L^s(R^3)), for 12/7 < s ≤ 12/5.

  • Subjects / Keywords
  • Graduation date
    Spring 2024
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/r3-jz23-f352
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.