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Asymmetric solutions of Burgers system with no-slip boundary condition. (Russian) Zbl 0978.76020

Andreev, V. K. (ed.) et al., Symmetry and differential equations. Proceedings of the 2nd international conference, Krasnoyarsk, Russia, August 21-25, 2000. Krasnoyarsk: Institute of Computational Modelling, Krasnoyarsk State Univ., Krasnoyarsk State Academy of Architecture and Civil Engineering, International Academy of Sciences of High School, 221-223 (2000).
The author constructs a solution for Cauchy problem for two-dimensional Burgers system (a model system for viscous flows) \(u_t+ uu_x+ vu_y= \mu\Delta u\), \(v_t+ uv_x+ vv_y= \mu\Delta v\) with no-slip boundary conditions. The construction uses projections on subspaces of functions satisfying homogeneous boundary conditions.
For the entire collection see [Zbl 0956.00040].

MSC:

76D99 Incompressible viscous fluids
35Q53 KdV equations (Korteweg-de Vries equations)
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