Existence and stability of noncharacteristic boundary-layers for the compressible Navier-Stokes and viscous MHD equations

Details Existence and stability of noncharacteristic boundary-layers for the compressible Navier-Stokes and viscous MHD equations Existence and stability of noncharacteristic boundary-layers for the compressible Navier-Stokes and viscous MHD equations

2008-05-21

arxiv.org/abs/0805.3333v1

Mathematics

Analysis of PDEs

Scientific paper

For a general class of hyperbolic-parabolic systems including the compressible Navier-Stokes and compressible MHD equations, we prove existence and stability of noncharacteristic viscous boundary layers for a variety of boundary conditions including classical Navier-Stokes boundary conditions. Our first main result, using the abstract framework established by the authors in the companion work \cite{GMWZ6}, is to show that existence and stability of arbitrary amplitude exact boundary-layer solutions follow from a uniform spectral stability condition on layer profiles that is expressible in terms of an Evans function (uniform Evans stability). Whenever this condition holds we give a rigorous description of the small viscosity limit as the solution of a hyperbolic problem with "residual" boundary conditions. Our second is to show that uniform Evans stability for small-amplitude layers is equivalent to Evans stability of the limiting constant layer, which in turn can be checked by a linear-algebraic computation. Finally, for a class of symmetric-dissipative systems including the physical examples mentioned above, we carry out energy estimates showing that constant (and thus small-amplitude) layers always satisfy uniform Evans stability. This yields existence of small-amplitude multi-dimensional boundary layers for the compressible Navier-Stokes and MHD equations. For both equations these appear to be the first such results in the compressible case.

Affiliated with

Also associated with

No associations

Rating

Existence and stability of noncharacteristic boundary-layers for the compressible Navier-Stokes and viscous MHD equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Existence and stability of noncharacteristic boundary-layers for the compressible Navier-Stokes and viscous MHD equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Existence and stability of noncharacteristic boundary-layers for the compressible Navier-Stokes and viscous MHD equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-290742