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In this paper, we consider the asymptotic behavior of an incompressible fluid around a bounded obstacle. By adapting the Schauder's estimate for stationary Navier–Stokes equation to improve the regularity, the problem is solved by using appropriate Carleman estimates. It should be noted that the minimal decaying rate for a general scalar equation is . However, the structure of the Navier–Stokes is special. Under the assumption for any nontrivial solution to be uniform bounded which is weaker than those in [10], we got the minimal decaying rate is which is better than the results in general scalar cases. 相似文献
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Ball convergence results are very important, since they demonstrate the complexity in choosing initial points for iterative methods. One of the most important problems in the study of iterative methods is to determine the convergence ball. This ball is small in general restricting the choice of initial points. We address this problem in the case of Wang’s method utilized to determine a zero of a derivative. Finding such a zero has many applications in computational fields, especially in function optimization. In particular, we find the convergence ball of Wang’s method using hypotheses up to the second derivative in contrast to earlier studies using hypotheses up to the fourth derivative. This way, we also extend the applicability of Wang’s method. Numerical experiments used to test the convergence criteria complete this study. 相似文献
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Jules K. Djoko Virginie S. Konlack Mohamed Mbehou 《Numerical Methods for Partial Differential Equations》2020,36(1):86-117
In this work, we consider the heat equation coupled with Stokes equations under threshold type boundary condition. The conditions for existence and uniqueness of the weak solution are made clear. Next we formulate the finite element problem, recall the conditions of its solvability, and study its convergence by making use of Babuska–Brezzi's conditions for mixed problems. Third we formulate an Uzawa's type iterative algorithm that separates the fluid from heat conduction, study its feasibility, and convergence. Finally the theoretical findings are validated by numerical simulations. 相似文献
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Djamel Ait-Akli & Abdelkader Merakeb 《偏微分方程(英文版)》2020,33(1):64-92
In this paper we consider the Lamé system on a polygonal convex domain
with mixed boundary conditions of Dirichlet-Neumann type. An explicit L2 norm
estimate for the gradient of the solution of this problem is established. This leads to an
explicit bound of the H1 norm of this solution. Note that the obtained upper-bound is
not optimal. 相似文献