메뉴 건너뛰기




Volumn 44, Issue 2, 2001, Pages 141-177

On the existence of a solution to stochastic Navier-Stokes equations

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; INCOMPRESSIBLE FLOW; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; NAVIER STOKES EQUATIONS; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; THEOREM PROVING;

EID: 0342903113     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(99)00255-2     Document Type: Article
Times cited : (44)

References (38)
  • 2
    • 0342674919 scopus 로고
    • A model of stochastic differential equation in Hilbert space applicable to Navier-Stokes equation in dimension 2
    • in: E. Mayer-Wolf, E. Merzbach, A. Schwartz (Eds.) Academic Press, New York
    • A. Bensoussan, A model of stochastic differential equation in Hilbert space applicable to Navier-Stokes equation in dimension 2, in: E. Mayer-Wolf, E. Merzbach, A. Schwartz (Eds.), Stochastic Analysis, Liber Amicorum for Moshe Zakai, Academic Press, New York, 1991, pp. 51-73.
    • (1991) Stochastic Analysis, Liber Amicorum for Moshe Zakai , pp. 51-73
    • Bensoussan, A.1
  • 3
    • 0001159580 scopus 로고
    • Equations stochastiques du type Navier-Stokes
    • Bensoussan A., Temam R. Equations stochastiques du type Navier-Stokes. J. Funct. Anal. 13:1973;195-222.
    • (1973) J. Funct. Anal. , vol.13 , pp. 195-222
    • Bensoussan, A.1    Temam, R.2
  • 5
    • 0000719751 scopus 로고    scopus 로고
    • On the stochastic Korteweg-de Vries equation
    • A. de Bouard, A. Debussche, On the stochastic Korteweg-de Vries equation, J. Funct. Anal. 154 (1998) 215-251.
    • (1998) J. Funct. Anal. , vol.154 , pp. 215-251
    • De Bouard, A.1    Debussche, A.2
  • 9
    • 0040560237 scopus 로고
    • Navier-Stokes equations with multiplicative noise
    • Capiński M., Cutland N.J. Navier-Stokes equations with multiplicative noise. Nonlinearity. 6:1993;71-77.
    • (1993) Nonlinearity , vol.6 , pp. 71-77
    • Capiński, M.1    Cutland, N.J.2
  • 11
    • 43949156954 scopus 로고
    • Stochastic equations in Hilbert space with application to Navier-Stokes equations in any dimension
    • Capiński M., Ga̧tarek D. Stochastic equations in Hilbert space with application to Navier-Stokes equations in any dimension. J. Funct. Anal. 126:1994;26-35.
    • (1994) J. Funct. Anal. , vol.126 , pp. 26-35
    • Capiński, M.1    Ga̧tarek, D.2
  • 12
    • 0003254999 scopus 로고
    • Stochastic partial differential equations in turbulence
    • in: A.T. Bharucha-Reid (Ed.) Academic Press, New York
    • P.L. Chow, Stochastic partial differential equations in turbulence, in: A.T. Bharucha-Reid (Ed.), Probabilistic Analysis and Related Topics, Vol. 1, Academic Press, New York, 1978, pp. 1-43.
    • (1978) Probabilistic Analysis and Related Topics , vol.1 , pp. 1-43
    • Chow, P.L.1
  • 13
    • 0029676645 scopus 로고    scopus 로고
    • A diffusion-approximation theorem in Navier-Stokes equation
    • Clouet J.F. A diffusion-approximation theorem in Navier-Stokes equation. Stochastic Anal. Appl. 14:1996;33-46.
    • (1996) Stochastic Anal. Appl. , vol.14 , pp. 33-46
    • Clouet, J.F.1
  • 14
  • 15
    • 0001820696 scopus 로고
    • Stochastic Burgers equation with correlated noise
    • Da Prato G., Gatarek D. Stochastic Burgers equation with correlated noise. Stochastics Stochastics Rep. 52:1995;29-41.
    • (1995) Stochastics Stochastics Rep. , vol.52 , pp. 29-41
    • Da Prato, G.1    Gatarek, D.2
  • 16
    • 0001241006 scopus 로고
    • Regularity of solutions of linear stochastic equations in Hilbert spaces
    • Da Prato G., Kwapień S., Zabczyk J. Regularity of solutions of linear stochastic equations in Hilbert spaces. Stochastics. 23:1987;1-23.
    • (1987) Stochastics , vol.23 , pp. 1-23
    • Da Prato, G.1    Kwapień, S.2    Zabczyk, J.3
  • 19
    • 0001262773 scopus 로고
    • Spatially homogeneous random evolutions
    • Dawson D.A., Salehi H. Spatially homogeneous random evolutions. J. Multivariate Anal. 10:1980;141-180.
    • (1980) J. Multivariate Anal. , vol.10 , pp. 141-180
    • Dawson, D.A.1    Salehi, H.2
  • 20
    • 21844520649 scopus 로고
    • Martingale and stationary solutions for stochastic Navier-Stokes equations
    • Flandoli F., Gatarek D. Martingale and stationary solutions for stochastic Navier-Stokes equations. Probab. Theory Related Fields. 102:1995;367-391.
    • (1995) Probab. Theory Related Fields , vol.102 , pp. 367-391
    • Flandoli, F.1    Gatarek, D.2
  • 23
    • 0002930573 scopus 로고
    • On weak solutions of stochastic equations in Hilbert spaces
    • Gatarek D., Goldys B. On weak solutions of stochastic equations in Hilbert spaces. Stochastics Stochastics Rep. 46:1993;41-51.
    • (1993) Stochastics Stochastics Rep. , vol.46 , pp. 41-51
    • Gatarek, D.1    Goldys, B.2
  • 26
    • 21344455684 scopus 로고
    • A stochastic Navier-Stokes equation for the vorticity of a two-dimensional fluid
    • Kotelenez P. A stochastic Navier-Stokes equation for the vorticity of a two-dimensional fluid. Ann. Appl. Probab. 7:1995;1126-1160.
    • (1995) Ann. Appl. Probab. , vol.7 , pp. 1126-1160
    • Kotelenez, P.1
  • 28
    • 0004198869 scopus 로고
    • Cambridge University Press, Cambridge
    • Y. Meyer, Wavelets and Operators, Cambridge University Press, Cambridge, 1992.
    • (1992) Wavelets and Operators
    • Meyer, Y.1
  • 30
    • 0001146109 scopus 로고
    • Existence and uniqueness of the solution for stochastic equations on Banach spaces
    • Peszat S. Existence and uniqueness of the solution for stochastic equations on Banach spaces. Stochastics Stochastics Rep. 55:1995;167-193.
    • (1995) Stochastics Stochastics Rep. , vol.55 , pp. 167-193
    • Peszat, S.1
  • 31
    • 0343545079 scopus 로고    scopus 로고
    • Sobolev spaces of functions on an infinite-dimensional domain
    • in: H.J. Engelbert, H. Föllmer, J. Zabczyk (Eds.) Gordon and Breach Publishers, Amsterdam
    • S. Peszat, Sobolev spaces of functions on an infinite-dimensional domain, in: H.J. Engelbert, H. Föllmer, J. Zabczyk (Eds.), Stochastic Processes and Related Topics Stochastic Monographs, Vol. 10, Gordon and Breach Publishers, Amsterdam, 1996, pp. 103-116.
    • (1996) Stochastic Processes and Related Topics Stochastic Monographs , vol.10 , pp. 103-116
    • Peszat, S.1
  • 32
    • 0031574567 scopus 로고    scopus 로고
    • Stochastic evolution equations with a spatially homogeneous Wiener process
    • Peszat S., Zabczyk J. Stochastic evolution equations with a spatially homogeneous Wiener process. Stochastic Processes Appl. 72:1997;187-204.
    • (1997) Stochastic Processes Appl. , vol.72 , pp. 187-204
    • Peszat, S.1    Zabczyk, J.2
  • 34
    • 0031145245 scopus 로고    scopus 로고
    • Qualitative properties for the stochastic Navier-Stokes equation
    • Schmalfuss B. Qualitative properties for the stochastic Navier-Stokes equation. Nonlinear Anal. Theory Methods Appl. 28:1997;1545-1563.
    • (1997) Nonlinear Anal. Theory Methods Appl. , vol.28 , pp. 1545-1563
    • Schmalfuss, B.1
  • 37
    • 0343545071 scopus 로고
    • Solutions statistiques homogènes des systèmes paraboliques et du système de Navier-Stokes
    • Vishik M.I., Foursikov A.V. Solutions statistiques homogènes des systèmes paraboliques et du système de Navier-Stokes. Ann. Scuola Norm. Super. Pisa. 4:1977;531-576.
    • (1977) Ann. Scuola Norm. Super. Pisa , vol.4 , pp. 531-576
    • Vishik, M.I.1    Foursikov, A.V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.