Exact controllability in projections for three-dimensional Navier-Stokes equations TeX Export

@misc{citeulike:452577, abstract = {The paper is devoted to studying controllability properties for 3D Navier-Stokes equations in a bounded domain. We establish a sufficient condition under which the problem in question is exactly controllable in any finite-dimensional projection. Our sufficient condition is verified for any torus in \$R^3\$. The proofs are based on a development of a general approach introduced by Agrachev and Sarychev in the 2D case. As a simple consequence of the result on controllability, we show that the Cauchy problem for the 3D Navier-Stokes system has a unique strong solution for any initial function and a large class of external forces.}, archivePrefix = {arXiv}, author = {Shirikyan, Armen}, citeulike-article-id = {452577}, citeulike-linkout-0 = {http://arxiv.org/abs/math/0512600}, citeulike-linkout-1 = {http://arxiv.org/pdf/math/0512600}, day = {27}, eprint = {math/0512600}, keywords = {3d, control, navier-stokes}, month = {Dec}, posted-at = {2005-12-29 13:35:51}, priority = {2}, title = {Exact controllability in projections for three-dimensional Navier-Stokes equations}, url = {http://arxiv.org/abs/math/0512600}, year = {2005} }

TY - ELEC ID - citeulike:452577 L3 - citeulike-article-id:452577 N2 - The paper is devoted to studying controllability properties for 3D Navier-Stokes equations in a bounded domain. We establish a sufficient condition under which the problem in question is exactly controllable in any finite-dimensional projection. Our sufficient condition is verified for any torus in $R^3$. The proofs are based on a development of a general approach introduced by Agrachev and Sarychev in the 2D case. As a simple consequence of the result on controllability, we show that the Cauchy problem for the 3D Navier-Stokes system has a unique strong solution for any initial function and a large class of external forces. TI - Exact controllability in projections for three-dimensional Navier-Stokes equations KW - 3d KW - control KW - navier-stokes AU - Shirikyan, Armen PY - 2005/Dec/27/ UR - http://arxiv.org/abs/math/0512600 ER -