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@ARTICLE{0951-7715-23-12-005,
    author = {Muzereau, Olivier and Neustupa, Jiř{\'{\i}} and Penel, Patrick},
     title = {A partially strong solution to the steady Navier–Stokes equations for compressible barotropic fluid with generalized impermeability boundary conditions},
   journal = {Nonlinearity},
    volume = {23},
    number = {12},
      year = {2010},
     pages = {3071},
       url = {http://stacks.iop.org/0951-7715/23/i=12/a=005},
  abstract = {We prove the existence of a partially strong solution to the steady Navier–Stokes equations for barotropic compressible fluid in a bounded simply connected domain with the prescribed generalized impermeability conditions u {\textperiodcentered} n = 0, curl u {\textperiodcentered} n = 0 and curl 2 u {\textperiodcentered} n = 0 on the boundary. We assume that the state law for the pressure has the form ##IMG## [http://ej.iop.org/images/0951-7715/23/12/005/non335132in001.gif] {{\cal P}(\rho)=\rho^{\gamma}} for γ > 3. We call the solution 'partially strong' because only the divergence-free part of velocity and the effective pressure have regularity typical for strong solutions, while the gradient part of velocity and the density have regularity typical for weak solutions.}
}