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21.
Kazuo Yamazaki 《随机分析与应用》2019,37(3):412-444
The magnetohydrodynamics system consists of the Navier-Stokes equations from fluid mechanics, coupled with the Maxwell’s equations from electromagnetism through multiples of non-linear terms involving derivatives. Following the approach of [1], we prove the existence of a unique invariant measure in case the forcing terms consist of the cylindrical Wiener processes with only low modes. Its proof requires taking advantage of the structure of the non-linear terms carefully and is extended to various other related models such as the magnetohydrodynamics-Boussinesq system from fluid mechanics in atmosphere and oceans, as well as the magneto-micropolar fluid system from the theory of microfluids. 相似文献
22.
In this paper, we derive the non-singular Green’s functions for the unbounded Poisson equation in one, two and three dimensions using a spectral cut-off function approach to impose a minimum length scale in the homogeneous solution. The resulting non-singular Green’s functions are relevant to applications which are restricted to a minimum resolved length scale (e.g. a mesh size ) and thus cannot handle the singular Green’s function of the continuous Poisson equation. We furthermore derive the gradient vector of the non-singular Green’s function, as this is useful in applications where the Poisson equation represents potential functions of a vector field. 相似文献
23.
Under some assumptions we find a general solution of the factorization problem for a family of second order difference equations. 相似文献
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25.
缪正武 《浙江大学学报(理学版)》2019,46(6):680-685
提出利用拉格朗日乘子法重新证明σ 2 ![]()
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算子的最优凹性,并定义了一个凸锥Γ 3 ? = λ = ( λ 1 , λ 2 , ? , λ n ) ∈ R n : σ 1 ( λ ) > 0 , σ 2 ( λ | i ) > 0 , 1 ≤ i ≤ n ![]()
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。利用σ 2 ![]()
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算子的最优凹性,给出了σ 2 H e s s i a n 方 程 P o g o r e l o v ![]()
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型C 2 ![]()
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内估计,进而证明了σ 2 ( D 2 u ( x ) ) = 1 , x ∈ R n ![]()
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的满足二次多项式增长条件的Γ 3 ? - ![]()
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凸整解为二次多项式。 相似文献
26.
《Physics letters. A》2019,383(20):2370-2375
We consider a bosonic Josephson junction in the Bose-Hubbard two-mode approximation where some of the parameters are corrupted by physically meaningful noise processes and study the corresponding relaxation dynamics towards its equilibrium state. We show with numerical simulations that this model can essentially capture all the important features observed in a recent experiment regarding the relaxation dynamics in one-dimensional bosonic Josephson junctions, namely the damped oscillations of the population imbalance and the relative phase, as well as the large final coherence factor. We expect that this work will further motivate research about the origin of relaxation mechanism in these systems. 相似文献
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29.
We look for positive solutions for the singular equation where , , is a parameter, and has some summability properties. By using a perturbation method and critical point theory, we obtain two solutions when and the parameter is small. 相似文献
30.
In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation with the critical situation that on g and p, where , is periodic and is bounded. 相似文献