Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Global Well-Posedness for Certain Density-Dependent Modified-Leray-α Models | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2011 Article ID 946208 7 pages doi 2011 946208 Research Article Global Well-Posedness for Certain Density-Dependent Modified-Leray-a Models Wenying Chen1 and Jishan Fan2 3 1 College of Mathematics and Computer Science Chongqing Three Gorges University Wanzhou Chongqing 404000 China 2 Department of Applied Mathematics Nanjing Forestry University Nanjing 210037 China 3 Department of Mathematics Hokkaido University Sapporo 060-0810 Japan Correspondence should be addressed to Wenying Chen wenyingchenmath@ Received 3 October 2010 Accepted 16 January 2011 Academic Editor R. N. Mohapatra Copyright 2011 W. Chen and J. Fan. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Global well-posedness result is established for both a 3D density-dependent modified-Leray-a model and a 3D density-dependent modified-Leray-a-MHD model. 1. Introduction A density-dependent Leray-a model can be written as pt div pu 0 pvt pu Vv Vn - Av 0 v 1 - a1 Au in 0 to X Q div v div u 0 in 0 to X Q v u 0 on 0 to X dQ p pv Co pq pqvq in Q c R3 where p is the fluid density v is the fluid velocity field u is the filtered fluid velocity and n is the pressure which are unknowns. a is the lengthscale parameter that represents the width 2 Journal of Inequalities and Applications of the filter and for simplicity we will take a 1. Q c R3 is a bounded domain with smooth boundary dQ. When p 1 the above system reduces to the well-known Leray-a model and has been studied in 1 2 . When a 0 the above system reduces to the classical density-dependent Navier-Stokes equation which has received many studies 3-6 . Specifically it is proved in 3 4 that the density-dependent Navier-Stokes equations has a unique locally smooth solution p v if the following two .
