journal article Feb 01, 1994

Example of zero viscosity limit for two dimensional nonstationary Navier-Stokes flows with boundary

View at Publisher Save 10.1007/bf03167219
Topics

No keywords indexed for this article. Browse by subject →

References
17
[1]
K. Asano, Zero-viscosity limit of the incompressible Navier-Stokes equation 1. Preprint.
[2]
K. Asano, Zero-viscosity limit of the incompressible Navier-Stokes equation 2. Preprint.
[3]
P. C. Fife, Considerations regarding the mathematical basis for Prandtl’s boundary layer theory. Arch. Rational Mech. Anal.,28 (1968), 184–216. 10.1007/bf00250926
[4]
A. Friedman, Partial Differential Equations of Parabolic Type. Prentice-Hall, Englewood Cliffs, 1964.
[5]
K.K. Golovkin, Vanishing viscosity in Cauchy’s problem for hydrodynamics equations. Proc. Steklov Inst. Math.,92 (1966), 33–53.
[6]
T. Kato, On classical solution for the two-dimensional non-stationary Euler equation. Arch. Rational Mech. Anal.,25 (1967), 188–200. 10.1007/bf00251588
[7]
T. Kato, Non-stationary flows of viscous and ideal fluids inR 3. J. Funct. Anal.,9 (1972), 296–305. 10.1016/0022-1236(72)90003-1
[8]
T. Kato, Quasi-linear equations of evolution with applications to partial differential equations. Lecture Notes in Math. vol. 448, Springer, 1975, 25–70. 10.1007/bfb0067080
[9]
T. Kato, Remarks on zero viscosity limit for nonstationary Navier-Stokes flows with boundary. Seminar on Nonlinear Partial Differential Equation (ed. S.S. Chern), Springer, 1982, 85–98. 10.1007/978-1-4612-1110-5_6
[10]
T. Kato and H. Fujita, On the nonstationary Navier-Stokes system. Rend. Sem. Mat. Univ. Padova,32 (1962), 243–260.
[11]
O.A. Ladyženskaja, V.A. Solonnikov and N.N. Ural’ceva, Linear and Quasilinear Equations of Parabolic Type. Amer. Math. Soc., 1968.
[12]
A. Majida, Vorticity and the mathematical theory of incompressible fluid flow. Comm. Pure Appl. Math.,39 (1986), 187–220. 10.1002/cpa.3160390711
[13]
S. Matsui and T. Shirota, On Prandtl boundary layer problem. Recent Topics in Nonlinear PDEII,. Kinokuniya/North-Holland Tokyo/Amsterdam, 1985, 81–105.
[14]
F.J. McGrath, Non-stationary plane flow of viscous and ideal fluids. Arch. Rational Mech. Anal.,27 (1968), 329–348. 10.1007/bf00251436
[15]
O.A. Oleinik and S.N. Kruzhkov, Quasi-linear second order parabolic equations with many independent variables. Russian Math. Surveys,16 (1961), 106–146. 10.1070/rm1961v016n05abeh004114
[16]
J. Serrin, On the mathematical basis for Prandtl’s boundary layer theory: an example. Arch. Rational Mech. Anal.,28 (1968), 217–225. 10.1007/bf00250927
[17]
H. Swann, The convergence with vanishing viscosity of non-stationary Navier-Stokes flow to ideal flow inR 3. Trans. Amer. Math. Soc.,157 (1971), 373–397.
Cited By
30
Journal of Mathematical Fluid Mecha...
SIAM Journal on Mathematical Analys...
The vanishing viscosity limit for some symmetric flows

Gung-Min Gie, James P. Kelliher · 2019

Annales de l'Institut Henri Poincar...
Communications in Partial Different...
Communications in Mathematical Phys...
Bulletin of the Brazilian Mathemati...
Physica D: Nonlinear Phenomena
Metrics
30
Citations
17
References
Details
Published
Feb 01, 1994
Vol/Issue
11(1)
Pages
155-170
License
View
Cite This Article
Shin’ya Matsui (1994). Example of zero viscosity limit for two dimensional nonstationary Navier-Stokes flows with boundary. Japan Journal of Industrial and Applied Mathematics, 11(1), 155-170. https://doi.org/10.1007/bf03167219