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Helmholtz decomposition
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<p>In <a href="/facts/Physics/a7aH2y08">physics</a> and <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the Helmholtz decomposition theorem or the fundamental theorem of vector calculus states that certain differentiable <a href="/facts/Vector_field/ccFNuPPp">vector fields</a> can be resolved into the sum of an <a href="/facts/Irrotational_vector_field/MoS3V9aV">irrotational</a> (<a href="/facts/Curl_(mathematics)/GuS8dc7o">curl</a>-free) vector field and a <a href="/facts/Solenoidal/9ohQ6clr">solenoidal</a> (<a href="/facts/Divergence/zpwwkFoU">divergence</a>-free) vector field. In <a href="/facts/Physics/a7aH2y08">physics</a>, often only the decomposition of sufficiently <a href="/facts/Smooth_function/mffL4ch2">smooth</a>, rapidly decaying <a href="/facts/Vector_field/ccFNuPPp">vector fields</a> in three dimensions is discussed. It is named after <a href="/facts/Hermann_von_Helmholtz/oFISedae">Hermann von Helmholtz</a>. </p>