کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4610186 1338549 2013 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Global well-posedness for the 2D Boussinesq system with anisotropic viscosity and without heat diffusion
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Global well-posedness for the 2D Boussinesq system with anisotropic viscosity and without heat diffusion
چکیده انگلیسی

We establish global existence and uniqueness theorems for the two-dimensional non-diffusive Boussinesq system with anisotropic viscosity acting only in the horizontal direction, which arises in ocean dynamics models. Global well-posedness for this system was proven by Danchin and Paicu; however, an additional smoothness assumption on the initial density was needed to prove uniqueness. They stated that it is not clear whether uniqueness holds without this additional assumption. The present work resolves this question and we establish uniqueness without this additional assumption. Furthermore, the proof provided here is more elementary; we use only tools available in the standard theory of Sobolev spaces, and without resorting to para-product calculus. We use a new approach by defining an auxiliary “stream-function” associated with the density, analogous to the stream-function associated with the vorticity in 2D incompressible Euler equations, then we adapt some of the ideas of Yudovich for proving uniqueness for 2D Euler equations.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 255, Issue 9, 1 November 2013, Pages 2636–2654
نویسندگان
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