<oai_dc:dc xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
<dc:title>Hadamard variational formula for the Green function for the velocity and pressure of the Stokes equations</dc:title>
<dc:creator>Erika Ushikoshi</dc:creator>
<dc:subject>35Q30</dc:subject><dc:subject>35J25</dc:subject><dc:subject>35C20</dc:subject><dc:subject>76D05</dc:subject><dc:subject>76D07</dc:subject><dc:subject>Hadamard variational formula</dc:subject><dc:subject>Stokes equations</dc:subject>
<dc:description>We consider the Hadamard variational formula for the Green function of the Stokes equations $\{\boldsymbol{G},R\}$ which describes the motion of the incompressible fluids moving slowly in the bounded domain $\Omega$ with the smooth boundary $\partial\Omega$. Under the perturbation of domains keeping those volumes and topological types invariant, we not only refine the proof of its formula for the velocity $G$ but we also develop a new formula for the pressure $R$. Our result may be regarded as the Hadamard variational formula for the Green functions as an example of the elliptic system of equations with the Dirichlet boundary condition.</dc:description>
<dc:publisher>Indiana University Mathematics Journal</dc:publisher>
<dc:date>2013</dc:date>
<dc:type>text</dc:type>
<dc:format>pdf</dc:format>
<dc:identifier>10.1512/iumj.2013.62.5033</dc:identifier>
<dc:source>10.1512/iumj.2013.62.5033</dc:source>
<dc:language>en</dc:language>
<dc:relation>Indiana Univ. Math. J. 62 (2013) 1315 - 1379</dc:relation>
<dc:coverage>state-of-the-art mathematics</dc:coverage>
<dc:rights>http://iumj.org/access/</dc:rights>
</oai_dc:dc>