共查询到20条相似文献,搜索用时 593 毫秒
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Oh Sung Kwon Jae Ryong Kweon 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(5):2936-2956
We show existence and regularity for the boundary value problems of the Navier–Stokes equations with non-standard BCs on a bounded plane domain with non-convex corners. We assign the vorticity value and the velocity normal component over the non-convex corner, the dynamic pressure value over inflow and outflow boundaries, and so on. We construct the corner singularity functions for the Stokes operator with zero vorticity and velocity normal component BCs, subtract its leading singularity from the solution by defining the coefficient of the singularity and show increased regularity for the remainder. The solution is determined by the smoother part and the coefficients of the singularities. It is seen from the singularity that the dynamic pressure has a transition layer that changes the sign (at in the domain). The obtained results can be applied to general polygonal domains and the cavity flows. 相似文献
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In a previous work, it was shown how the linearized strain tensor field can be considered as the sole unknown in the Neumann problem of linearized elasticity posed over a domain , instead of the displacement vector field in the usual approach. The purpose of this Note is to show that the same approach applies as well to the Dirichlet–Neumann problem. To this end, we show how the boundary condition on a portion of the boundary of Ω can be recast, again as boundary conditions on , but this time expressed only in terms of the new unknown . 相似文献
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《Applied Mathematics Letters》2006,19(11):1249-1254
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In this paper we investigate the existence of a unique global mild solution in of the initial-boundary value problem associated with the logarithmic Schrödinger equation , with and . 相似文献
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Nicolas Nisse 《Discrete Applied Mathematics》2009,157(12):2603-2610
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Mourad Ben Slimane Hnia Ben Braiek 《Journal of Mathematical Analysis and Applications》2012,396(1):21-48
In this paper, we prove that anisotropic homogeneous Besov spaces are gentle spaces, for all parameters and all anisotropies . Using the Littlewood–Paley decomposition, we study their completeness, separability, duality and homogeneity. We then define the notion of anisotropic orthonormal wavelet basis of , and we show that the homogeneous version of Triebel families of anisotropic orthonormal wavelet bases associated to the tensor product of Lemarié–Meyer (resp. Daubechies) wavelets are particular examples. We characterize the spaces using Lemarié–Meyer wavelets. In fact, we show that these bases will be either unconditional bases or unconditional -weak bases of , depending on whether is separable or not. By introducing an anisotropic version of the class of almost diagonal matrices related to anisotropic orthonormal wavelet bases, we prove that these spaces are stable under changes of anisotropic orthonormal wavelet bases. As a consequence, we extend the characterization of using Daubechies wavelets. 相似文献
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Quốc Anh Ngô 《Comptes Rendus Mathematique》2017,355(5):526-532
In this note, we mainly study the relation between the sign of and in with and for . Given the differential inequality , first we provide several sufficient conditions so that holds. Then we provide conditions such that for all , which is known as the sub poly-harmonic property for u. In the last part of the note, we revisit the super poly-harmonic property for solutions to and with in . 相似文献