Journal of Mathematical Physics, Volume 62, Issue 2, February 2021. In this paper, we establish the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear plane parallel flows of viscous incompressible magnetohydrodynamic flow with the no-slip boundary condition of velocity and perfectly conducting walls for magnetic fields. The convergence is shown under various Sobolev norms, including the physically important space–time uniform norm L∞(H1). In addition, similar convergence results are also obtained under the case with uniform magnetic fields. This implies the stabilizing effects of magnetic fields. Besides, the higher-order expansion is also considered.

## Authors

## Departments

## Libraries

## Recent Articles

- Stability of the boundary layer expansion for the 3D plane parallel MHD flow
- Particle–hole symmetries in condensed matter
- Revisiting Groeneveld’s approach to the virial expansion
- Diffusion of charge carriers in pentacene
- Large lattice-relaxation-induced intrinsic shallow p-type characteristics in monolayer black phosphorus and black arsenic
- Quantitative analysis of magnetic cobalt particles with an optically pumped atomic magnetometer
- Observation of electrically detected electron nuclear double resonance in amorphous hydrogenated silicon films
- Unconventional anomalous Hall effect in magnetic topological insulator MnBi4Te7 device
- Spectral imaging of flexible terahertz coding metasurface
- Ellipsometric study of the electronic behaviors of titanium-vanadium dioxide (TixV1−xO2) films for 0 ≤ x ≤ 1 during semiconductive-to-metallic phase transition
- SO(9) characterization of the standard model gauge group
- Rigorous results for the electrical conductivity due to electron–phonon scattering
- A common parametrization for finite mode Gaussian states, their symmetries, and associated contractions with some applications
- Q&A: How Perseverance will build on past Martian expeditions
- Atomic and electronic structure of cesium lead triiodide surfaces
- Excited state dynamics of 7-deazaguanosine and guanosine 5′-monophosphate
- Graph analysis of proton conduction pathways in scandium-doped barium zirconate
- n-decane diffusion in carbon nanotubes with vibration
- Formation of negative and positive ions in the radiosensitizer nimorazole upon low-energy electron collisions
- Sampling initial positions and momenta for nuclear trajectories from quantum mechanical distributions