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Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 1
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Articles

Local well-posedness for 2D incompressible magneto-micropolar boundary layer system

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Pages 206-227 | Received 28 Jan 2019, Accepted 15 Mar 2019, Published online: 26 Mar 2019

References

  • Xue LT. Wellposedness and zero microrotation viscosity limit of the 2D micropolar fluid equations. Math Methods Appl Sci. 2011;34(14):1760–1777. doi: 10.1002/mma.1491
  • Cheng JF, Liu YJ. Global regularity of the 2D magnetic micropolar fluid flows with mixed partial viscosity. Comput Math Appl. 2015;70(1):66–72. doi: 10.1016/j.camwa.2015.04.026
  • Lin HX, Xiang ZY. Global well-posedness for 2D incompressible magneto-micropolar fluid system with partial viscosity. Preprint; 2018.
  • Wang YZ, Wang YX. Blow-up criterion for two-dimensional magneto-micropolar fluid equations with partial viscosity. Math Methods Appl Sci. 2011;34(17):2125–2135. doi: 10.1002/mma.1510
  • Guo CC, Zhang ZJ, Wang JL. Regularity criteria for the 3D magneto-micropolar fluid equations in Besov spaces with negative indices. Appl Math Comput. 2012;218(21):10755–10758.
  • Jia Y. Existence theorem and blow-up criterion of the strong solutions to the magneto-micropolar fluid equations. Math Methods Appl Sci. 2010;31(9):1113–1130.
  • Ortega-Torres EE, Rojas-Medar MA. Magneto-micropolar fluid motion: global existence of strong solutions. Abstr Appl Anal. 1999;4(2):109–125. doi: 10.1155/S1085337599000287
  • Xiang ZY, Yang HZ. On the regularity criteria for the 3D magneto-micropolar fluids in terms of one directional derivative. Bound Value Probl. 2012;1(139):1–14.
  • Eringen AC. Theory of micropolar fluids. Indiana Univ Math J. 1965;16(1):42.
  • Berkovski B, Bashtovoy V. Magnetic fluids and applications handbook. New York (NY): Bell House; 1996.
  • Sava V. On the existence and uniqueness of the solution of a boundary-value problem in the theory of incompressible micropolar fluids. Differ Equ. 1973;49(5):645–653.
  • Sava VA. The initial-boundary-value problems in the theory of micropolar fluids. Z Angew Math Mech. 2010;58(11):511–518. doi: 10.1002/zamm.19780581106
  • Lin XY, Zhang T. Almost global existence for 2D magnetohydrodynamics boundary layer system. Math Methods Appl Sci. 2018;17(41):7530–7553. doi: 10.1002/mma.5217
  • Liu CJ, Xie F, Yang T. MHD boundary layers theory in Sobolev spaces without monotonicity. I. Well-posedness theory. Comm Pure Appl Math. 2019;72(1):63–121. doi: 10.1002/cpa.21763
  • Liu CJ, Xie F, Yang T. Justification of Prandtl ansatz for MHD boundary layer. arXiv:170400523. 2018. p. 1–34.
  • Liu CJ, Xie F, Yang T. Ill-posedness and well-posedness of the linearized MHD boundary layer equations. Preprint; 2017.
  • Oleinik OA, Samokhin VN. Mathematical models in boundary layer theory. Vol. 15. Roca Raton, London, New York, Washington, DC: Chapman & Hall, CRC; 1999.
  • Kukavica I, Vicol V. On the radius of analyticity of solutions to the three-dimensional Euler equations. Proc Am Math Soc. 2009;137(2):669–677. doi: 10.1090/S0002-9939-08-09693-7
  • Kukavica I, Vicol V. The domain of analyticity of solutions to the three-dimensional Euler equations in a half space. Discrete Contin Dyn – A. 2017;29(1):285–303. doi: 10.3934/dcds.2011.29.285
  • Kukavica I, Vicol V. On the local existence of analytic solutions to the Prandtl boundary layer equations. Commun Math Sci. 2012;11(11):269–292.
  • Ignatova M, Vicol V. Almost global existence for the Prandtl boundary layer equations. Arch Ration Mech Anal. 2016;2:809–848. doi: 10.1007/s00205-015-0942-2
  • Kukavica I, Vicol V, Fei W. The van Dommelen and Shen singularity in the Prandtl equations. Adv Math. 2017;307:288–311. doi: 10.1016/j.aim.2016.11.013

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