Building divergence free vector field
- Example: Define 2 scalar fields \((a,b)\)
- Build vector field \(u=\nabla a \times \nabla b\)
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- \({div}(u) = {div}(\nabla a \times \nabla b)\)
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- \(div(u) = \underbrace{curl(\nabla a)}_{=0} \cdot \nabla b - \nabla a\cdot \underbrace{curl(\nabla b)}_{=0}\)
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- \(div(u) = 0 \Rightarrow \) divergence free vector field
