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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The convergence with vanishing viscosity of nonstationary Navier-Stokes flow to ideal flow in $ R\sb{3}$


Author: H. S. G. Swann
Journal: Trans. Amer. Math. Soc. 157 (1971), 373-397
MSC: Primary 35.79; Secondary 76.00
MathSciNet review: 0277929
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Abstract: It is shown here that a unique solution to the Navier-Stokes equations exists in $ {R_3}$ for a small time interval independent of the viscosity and that the solutions for varying viscosities converge uniformly to a function that is a solution to the equations for ideal flow in $ {R_3}$. The existence of the solutions is shown by transforming the Navier-Stokes equations to an equivalent system solvable by applying fixed point methods with estimates derived from using semigroup theory.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0277929-7
PII: S 0002-9947(1971)0277929-7
Keywords: Navier-Stokes equations, viscous flow, Euler equations, ideal flow, potential theory, semigroups of operators, Sobolev space, nonlinear partial differential equations
Article copyright: © Copyright 1971 American Mathematical Society