- #1

Jhenrique

- 685

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If a vector field ##\vec{v}## is non-divergent, so the identity is satisfied: ##\vec{\nabla}\cdot\vec{v}=0##;

if is non-rotational: ##\vec{\nabla}\times\vec{v}=\vec{0}##;

but if is "non-linear"

Which differential equation the vector ##\vec{v}## satisfies?

EDIT: this isn't an arbritrary question, is an important question, because the Helmholtz-Hodge decomposition says that every vector field can be decompost in a divergent vector field + a rotational vector field + a linear vector field.

if is non-rotational: ##\vec{\nabla}\times\vec{v}=\vec{0}##;

but if is "non-linear"

Which differential equation the vector ##\vec{v}## satisfies?

EDIT: this isn't an arbritrary question, is an important question, because the Helmholtz-Hodge decomposition says that every vector field can be decompost in a divergent vector field + a rotational vector field + a linear vector field.

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