Some similarity solutions of the Navier-Stokes equations and related topics
نویسندگان
چکیده
We consider a semilinear equation arising from the Navier-Stokes equations { the governing equations of viscous uid motion { and related model equations. The solutions of the semilinear equation represent a certain class of exact solutions of the Navier-Stokes equations. Both the equation and our models have non-local terms. We will show that the non-locality will play an intriguing role for the blowup and/or global existence of the solutions and that the convection term, which is often neglected in the study of the blow-up problems, plays a very decisive role. In addition to our new contributions, open problems and known facts are surveyed. 1991 Mathematics Subject Classi cation. 35K55, 35Q30, 76D05.
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