<?xml version="1.0" encoding="UTF-8"?>
<?xml-stylesheet type="text/xsl" href="f2.xsl"?>
<top_article>
<mrnumber>MR2351212</mrnumber>
<author>Oleg ZUBELEVICH</author>
<author_utf8>Oleg ZUBELEVICH</author_utf8>
<title>On Analytic Solutions to the Navier-Stokes Equation in 3-D Torus</title>
<journal>Funkcialaj Ekvacioj. Serio Internacia</journal>
<volume>50</volume>
<year>2007</year>
<page>171--185</page>
<url_pdf>http://fe.math.kobe-u.ac.jp/FE/FullPapers/50-2/50_171.pdf</url_pdf>
<mathsci_link>http://www.ams.org/mathscinet-getitem?mr=MR2351212</mathsci_link>
<abstract>We consider NSE with $H^1$-initial conditions on the 3-dimensional torus and prove that there exists a solution that is analytic in all variables.</abstract>
<keywords>Navier-Stokes equation, Mathematical fluid, Fluid mechanics, Cauchy-Kovalevskaya problem.</keywords>
<subject>76D03.</subject>
<fesi_info>
  <FILE>50-171</FILE>
  <YEAR>2007</YEAR>
  <TITLE>On Analytic Solutions to the Navier-Stokes Equation in 3-D Torus</TITLE>
  <AUTHOR>Oleg ZUBELEVICH</AUTHOR>
  <AUTHOR_utf8>Oleg ZUBELEVICH</AUTHOR_utf8>
</fesi_info>

<references>

<article>
<bibitem>1</bibitem>
<author>Browder, F. E.</author>
<title>A new generalization of the Schauder fixed point theorem</title>
<journal>Math. Ann.</journal>
<vol>174</vol>
<year>1967</year>
<page>285-290</page>
<mr>MR0223944</mr>
</article>

<book>
<bibitem>2</bibitem>
<author>Constantin, P.; Foias, C.</author>
<booktitle>Navier-Stokes Equations</booktitle>
<publisher>Univ. of Chicago Press, Chicago</publisher>
<year>1988</year>
<mr>MR0972259</mr>
</book>

<article>
<bibitem>3</bibitem>
<author>Hopf, E.</author>
<title>&#220;ber die Anfangswertaufgabe f&#252;r die hydrodynamischen Grundgleichungen</title>
<journal>Math. Nachr.</journal>
<vol>4</vol>
<year>1951</year>
<page>213-231</page>
<mr>MR0050423</mr>
</article>

<article>
<bibitem>4</bibitem>
<author>Kahane, C.</author>
<title>On the spatial analyticity of solutions of the Navier-Stokes equations</title>
<journal>Arch. Rational Mech. Anal.</journal>
<vol>33</vol>
<year>1969</year>
<page>386-405</page>
<mr>MR0245989</mr>
</article>

<book>
<bibitem>5</bibitem>
<author>Ladyzhenskaya, O.</author>
<booktitle>The Mathematical Theory of Viscous Incompressible Flow</booktitle>
<publisher>Gordon and Breach, New York</publisher>
<year>1969</year>
<mr>MR0254401</mr>
</book>

<article>
<bibitem>6</bibitem>
<author>Lednev, N.</author>
<title>New method for solving PDE</title>
<journal>Math. Collection</journal>
<vol>22(64)</vol>
<year>1948</year>
<page>205-259 (in Russian)</page>
<mr>MR0027117</mr>
</article>

<article>
<bibitem>7</bibitem>
<author>Leray, J.</author>
<title>Essai sur le mouvement d'un liquide visqueux emplissant l'espace</title>
<journal>Acta Math.</journal>
<vol>63</vol>
<year>1934</year>
<page>193-248</page>
<mr>MR1555394</mr>
</article>

<article>
<bibitem>8</bibitem>
<author>Masuda, K.</author>
<title>On the analyticity and the unique continuation theorem for solutions of the Navier-Stokes equations</title>
<journal>Proc. Japan Acad.</journal>
<vol>43</vol>
<year>1967</year>
<page>827-832</page>
<mr>MR0247304</mr>
</article>

<article>
<bibitem>9</bibitem>
<author>Masuda, K.</author>
<title>On the regularity of solutions of the nonstationary Navier-Stokes equations</title>
<journal>Approx. methods for N.-Stokes problems, Lect. Notes in Math., 771</journal>
<year>1980</year>
<page>360-370</page>
<mr>MR0566007</mr>
</article>

<book>
<bibitem>10</bibitem>
<author>Nirenberg, L.</author>
<booktitle>Topics in Nonlinear Functional Analysis</booktitle>
<publisher>New York Univ.</publisher>
<year>1974</year>
<mr>MR0488102</mr>
</book>

<article>
<bibitem>11</bibitem>
<author>Nishida, T.</author>
<title>A note on a theorem of Nirenberg</title>
<journal>J. Differential Geometry</journal>
<vol>12</vol>
<year>1977</year>
<page>629-633</page>
<mr>MR0512931</mr>
</article>

<book>
<bibitem>12</bibitem>
<author>Temam, R.</author>
<booktitle>Navier-Stokes Equations: Theory and numerical analysis</booktitle>
<publisher>Volume 2 of Studies in Mathematics and its Applications, North-Holland Pablishing Co., Amsterdam-New York, revised edition</publisher>
<year>1979</year>
<mr>MR0603444</mr>
</book>

<book>
<bibitem>13</bibitem>
<author>Temam, R.</author>
<booktitle>Navier-Stokes Equations and Nonlinear Functional analysis</booktitle>
<publisher>Vol. 66 of CBMS-NSF Regional Conference Series in Applied Math. SIAM Philadelphia, PA, second edition</publisher>
<year>1995</year>
<mr>MR1318914</mr>
</book>

<article>
<bibitem>14</bibitem>
<author>Pronin, A.; Treschev, D.</author>
<title>Continuous averaging in multi-frequency slow-fast systems</title>
<journal>Regular and Chaotic Dynamics</journal>
<vol>5</vol>
<year>2000</year>
<page>157-170</page>
<mr>MR1780707</mr>
</article>

<article>
<bibitem>15</bibitem>
<author>Serrin, J.</author>
<title>The initial value problem for the Navier-Stokes equations</title>
<journal>Non-linear Problems R. E. Langer, ed., Univ. of Wisconsin Press</journal>
<year>1963</year>
<page>69-98</page>
<mr>MR0150444</mr>
</article>

<article>
<bibitem>16</bibitem>
<author>Serrin, J.</author>
<title>On the interior regularity of weak solutions of the Navier-Stokes equations</title>
<journal>Arch. Rational Mech. Anal.</journal>
<vol>9</vol>
<year>1962</year>
<page>187-195</page>
<mr>MR0136885</mr>
</article>

<book>
<bibitem>17</bibitem>
<author>Schwartz, L.</author>
<booktitle>Analyse Math&#233;matique</booktitle>
<publisher>Hermann</publisher>
<year>1967</year>
<mr>MR0226972</mr>
</book>

<book>
<bibitem>18</bibitem>
<author>Yosida, K.</author>
<booktitle>Functional Analysis</booktitle>
<publisher>Springer Verlag</publisher>
<year>1965</year>
<mr>MR0180824</mr>
</book>

<book>
<bibitem>19</bibitem>
<author>Yudovich, V. I.</author>
<booktitle>The linearization method in hydrodynamical stability theory</booktitle>
<publisher>American Math. Society, Providence, RI</publisher>
<year>1989</year>
<mr>MR1003607</mr>
</book>

<article>
<bibitem>20</bibitem>
<author>Zubelevich, O.</author>
<title>On the Magorant Method for Cauchy-Kovalevskaya Problem</title>
<journal>Mathematical Notes</journal>
<vol>69(3)</vol>
<year>2001</year>
<page>363-374 (in Russian)</page>
<mr>MR1846835</mr>
</article>

<article>
<bibitem>21</bibitem>
<author>Zubelevich, O.</author>
<title>A generalization of Schauder's theorem and its application to Cauchy-Kovalevskaya problem</title>
<journal>Electron. J. Diff. Eqns.</journal>
<vol>2003</vol>
<year>2003</year>
<page>No. 55, pp. 1-6</page>
<mr>MR1971121</mr>
</article>

</references>
</top_article>
