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On the vanishing viscosity in the Cauchy problem for the equations of a nonhomogeneous incompressible fluid

Published online by Cambridge University Press:  18 May 2009

Shigeharu Itoh
Shigeharu Itoh
Affiliation:
Department of Mathematics, Faculty of Education, Hirosaki University, Hirosaki 036, Japan
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Let us consider the Cauchy problem

in QT= ℝ3 × [0, T], where f(x, t), ρ0(x) and v0(x) are given, while the density ρ(x, t), the velocity vector v(x, t)= (υ1(x, t), υ2(x, t), υ3(x, t)) and the pressure p(x, t) are unknowns. The viscosity coefficient μ is assumed to be nonnegative. In these equations, the pressure p is automatically determined (up to a function of t) by ρ and v, namely, by solving the equation

Thus we mention (ρ, v) when we talk about the solution of (1.1:μ).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 1 , January 1994 , pp. 123 - 129
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

REFERENCES

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