Representation of vector fields
DOI:
https://doi.org/10.14419/gjma.v3i2.4577الكلمات المفتاحية:
Vector elds، Representation of vector elds.الملخص
A simple proof is given for the explicit formula which allows one to recover a \(C^2\) – smooth vector field \(A=A(x)\) in \(\mathbb{R}^3\), decaying at infinity, from the knowledge of its \(\nabla \times A\) and \(\nabla \cdot A\). The representation of \(A\) as a sum of the gradient field and a divergence-free vector fields is derived from this formula. Similar results are obtained for a vector field in a bounded \(C^2\) - smooth domain.
المراجع
[1] O. Ladyzhenskaya, The mathematical theory of viscous incompressible fluid, Gordon and Breach, New York, 1969.
[2] D. Menzel, Fundamental formulas of physics, Prentice Hall, New York, 1955.
[3] R. Temam, Navier-Stokes equations, North Holland, Amsterdam, 1984.
التنزيلات
منشور
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القسم
الرخصة
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