Access the full text.
Sign up today, get DeepDyve free for 14 days.
P. Grisvard (1985)
Elliptic Problems in Nonsmooth Domains
S. Kracmar, J. Neustupa (1994)
Modelling of flows of a viscous incompressible fluid through a channel by means of variational inequalitiesJournal of Applied Mathematics and Mechanics, 74
A. Kufner, O. John, S. Fučík (1977)
Function Spaces
R. Temam (1979)
Navier–Stokes Equations, Theory and Numerical Analysis
P. Kučera (1997)
Proc. 3rd Summer Conference ‘Numerical Modelling in Continuum Mechanics’
J. Lions, E. Magenes (1972)
Non-homogeneous boundary value problems and applications
H. Gajewski, K. Gröger, K. Zacharias (1978)
Nonlinear Operator Equations and Operator Differential Equations
J. Heywood, R. Rannacher, S. Turek (1996)
ARTIFICIAL BOUNDARIES AND FLUX AND PRESSURE CONDITIONS FOR THE INCOMPRESSIBLE NAVIER–STOKES EQUATIONSInternational Journal for Numerical Methods in Fluids, 22
T. Bratanow (1978)
Navier-Stokes equations: theory and numerical analysis: R. Teman North-Holland, Amsterdam and New York. 1977. 454 pp. US $45.00Applied Mathematical Modelling, 2
S. Kračmar, J. Neustupa (1994)
Modelling of flows of a viscous incompressible fluid through a channel by means of variational inequalitiesZ. angew. math. Mech., 74
H. Beckert (1973)
J. L. Lions and E. Magenes, Non‐Homogeneous Boundary Value Problems and Applications, II. (Die Grundlehren d. Math. Wissenschaften, Bd. 182). XI + 242 S. Berlin/Heidelberg/New York 1972. Springer‐Verlag. Preis geb. DM 58,—Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik, 53
We study the existence and uniqueness of solutions to the system of three-dimensionalNavier-Stokes equations and the continuity equation for incompressible fluid with mixedboundary conditions. It is known that if the Dirichlet boundary conditions are prescribed on thewhole boundary and the total influx equals zero, then weak solutions exist globally in time andthey are even unique and smooth in the case of two-dimensional domains. The methods that havebeen used to prove these results fail if non-Dirichlet conditions are applied on a part of theboundary, since there is then no control over the energy flux on this part of the boundary. In thispaper, we prove the existence and the uniqueness of solutions on a (short) time interval. Theproof is performed for Lipschitz domains and a wide class of initial data. The length of the timeinterval on which the solution exists depends only on certain norms of the data.
Acta Applicandae Mathematicae – Springer Journals
Published: Sep 18, 2004
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.