- #1
Jhenrique
- 685
- 4
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.
Last edited: