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Abstract. In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier—Stokes equation in bounded
and unbounded domains. These solutions are stochastic analogs of the classical Lions—Prodi solutions to the deterministic
Navier—Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability
space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions
to the Navier—Stokes martingale problem where the probability space is also obtained as a part of the solution. 相似文献
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R. Sritharan 《Discrete Mathematics》2008,308(12):2581-2588
Golumbic, Kaplan, and Shamir [Graph sandwich problems, J. Algorithms 19 (1995) 449-473], in their paper on graph sandwich problems published in 1995, left the status of the sandwich problems for strongly chordal graphs and chordal bipartite graphs open. It was recently shown [C.M.H. de Figueiredo, L. Faria, S. Klein, R. Sritharan, On the complexity of the sandwich problems for strongly chordal graphs and chordal bipartite graphs, Theoret. Comput. Sci., accepted for publication] that the sandwich problem for strongly chordal graphs is NP-complete. We show that given graph G with a proper vertex coloring c, determining whether there is a supergraph of G that is chordal bipartite and also is properly colored by c is NP-complete. This implies that the sandwich problem for chordal bipartite graphs is also NP-complete. 相似文献
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In an article Cheng (2009) [3] published recently in this journal, it was shown that when k≥3, the problem of deciding whether the distinguishing chromatic number of a graph is at most k is NP-hard. We consider the problem when k=2. In regards to the issue of solvability in polynomial time, we show that the problem is at least as hard as graph automorphism, but no harder than graph isomorphism. 相似文献
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We study the local exact controllability of the steady state solutions of the magnetohydrodynamic equations. The main result of the paper asserts that the steady state solutions of these equations are locally controllable if they are smooth enough. We reduce the local exact controllability of the steady state solutions of the magnetohydrodynamic equations to the global exact controllability of the null solution of the linearized magnetohydrodynamic system via a fixed‐point argument. The treatment of the reduced problem relies on two Carleman‐type inequalities for the backward adjoint system. © 2003 Wiley Periodicals, Inc. 相似文献
5.
A Wentzell–Freidlin type large deviation principle is established for the two-dimensional Navier–Stokes equations perturbed by a multiplicative noise in both bounded and unbounded domains. The large deviation principle is equivalent to the Laplace principle in our function space setting. Hence, the weak convergence approach is employed to obtain the Laplace principle for solutions of stochastic Navier–Stokes equations. The existence and uniqueness of a strong solution to (a) stochastic Navier–Stokes equations with a small multiplicative noise, and (b) Navier–Stokes equations with an additional Lipschitz continuous drift term are proved for unbounded domains which may be of independent interest. 相似文献
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V. Barbu S. S. Sritharan 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2003,130(4):449-461
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We show that if G is a bipartite graph with no induced cycles on exactly 6 vertices, then the minimum number of chain subgraphs of G needed to cover E(G) equals the chromatic number of the complement of the square of line graph of G. Using this, we establish that for a chordal bipartite graph G, the minimum number of chain subgraphs of G needed to cover E(G) equals the size of a largest induced matching in G, and also that a minimum chain subgraph cover can be computed in polynomial time. The problems of computing a minimum chain cover and a largest induced matching are NP-hard for general bipartite graphs. Finally, we show that our results can be used to efficiently compute a minimum chain subgraph cover when the input is an interval bigraph. 相似文献
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The grain growth dependence of microstructure and its effects on magnetic and transport properties are studied in the polycrystalline La0.67Ba0.33MnO3 oxides. It is found that a lateral growth manner along a certain direction and a concentric terrace pattern along three orthogonal axes occur in the samples sintered at 1573 and 1673 K, respectively. Lamella-like twin microstructure forms in the concentric terrace growth pattern and the magnetoresistance properties can be enhanced by the twin microstructure. It suggests that the twin-boundaries in twin-grains may possibly induce spin-dependent scattering of electrons that is field reduced, or spin-polarized tunneling of electrons that is field enhanced, thus strengthening the effect of grain boundaries. 相似文献