Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 29 Issue 1
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- Pages.125-135
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- 1992
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
ON THE SUFFICIENT CONDITION FOR THE LINEARIZED APPROXIMATION OF THE B$\"{E}$ NARD CONVECTION PROBLEM
- Song, Jong-Chul (Department of Mathematics, Hanyang University) ;
- Jeon, Chang-Ho (Department of Mathematics, Hanyang University)
- Published : 1992.02.01
Abstract
In various viscus flow problems it has been the custom to replace the convective derivative by the ordinary partial derivative in problems for which the data are small. In this paper we consider the Benard Convection problem with small data and compare the solution of this problem (assumed to exist) with that of the linearized system resulting from dropping the nonlinear terms in the expression for the convective derivative. The objective of the present work is to derive an estimate for the error introduced in neglecting the convective inertia terms. In fact, we derive an explicit bound for the L
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