Acta Mathematica Scientia最新文献

This paper is concerned with the Navier-Stokes/Allen-Cahn system, which is used to model the dynamics of immiscible two-phase flows. We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form of η(ρ) = ρ^α. The existence of unique global H^2m-solutions (m ∈ ℕ) to the free boundary problem is proven for when (0 < alpha < {1 over 4}). Furthermore, we obtain the global C^∞-solutions if the initial data is smooth.

This paper is devoted to the study of the shape of the free boundary for a three-dimensional axisymmetric incompressible impinging jet. To be more precise, we will show that the free boundary is convex to the fluid, provided that the uneven ground is concave to the fluid.

We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary ∂Ω is split into two disjoint parts and possesses different transmission conditions. Using the variational method, we obtain the well posedness of the interior transmission problem, which plays an important role in the proof of the discreteness of eigenvalues. Then we achieve the existence of an infinite discrete set of transmission eigenvalues provided that n ≡ 1, where a fourth order differential operator is applied. In the case of n ≢ 1, we show the discreteness of the transmission eigenvalues under restrictive assumptions by the analytic Fredholm theory and the T-coercive method.

We study the closed range property and the strict singularity of integration operators acting on the spaces F(p, pα − 2, s). We completely characterize the closed range property of the Volterra companion operator I_g on F(p, pα − 2, s), which generalizes the existing results and answers a question raised in [A. Anderson, Integral Equations Operator Theory, 69 (2011), no. 1, 87–99]. For the Volterra operator J_g, we show that, for 0 < α ≤ 1, J_g never has a closed range on F (p, pα − 2, s). We then prove that the notions of compactness, weak compactness and strict singularity coincide in the case of J_g acting on F(p,p − 2, s).

We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations. The estimates, based on either the continuously observed process or the discretely observed process, are considered. Under certain conditions, we prove the strong consistency and the asymptotic normality of the two estimators. Our method is also suitable for one-sided reflected stochastic differential equations. Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis et al. (Stat Sin, 2021, 31: 29–51). Several real data sets of the currency exchange rate are used to illustrate our proposed methodology.

In this paper, we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space ({mathbb{R}^3} times mathbb{T}). The semilinear nonlinearity is assumed to be of the cubic form. The main ingredient here is the establishment of the L²–L^∞ decay estimates and the energy estimates for the linear problem, which are adapted to the wave equation on the product space. The proof is based on the Fourier mode decomposition of the solution with respect to the periodic direction, the scaling technique, and the combination of the decay estimates and the energy estimates.

In this article, we study Kähler metrics on a certain line bundle over some compact Kähler manifolds to find complete Kähler metrics with positive holomorphic sectional (or bisectional) curvatures. Thus, we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.

In this paper, we study the asymptotic behavior of a class of inverse quotient curvature flow in the anti-de Sitter-Schwarzschild manifold. We prove that under suitable convex conditions for the initial hypersurface, one can get the long-time existence for the inverse curvature flow. Moreover, we also get that the principal curvatures of the evolving hypersurface converge to 1 when t → +∞.

In this paper, using Parseval frames we generalize Sun’s results to g-frames in Hilbert C*-modules. Moreover, for g-frames in Hilbert spaces, we present some characterizations in terms of a family of frames, not only for orthonormal bases. Also, we have a note about a comment and a relation in the proof of Proposition 5.3 in [D. Li et al., On weaving g-frames for Hilbert spaces, Complex Analysis and Operator Theory, 2020]. Finally, we have some results for g-Riesz bases, woven and P-woven g-frames.

In this paper, we prove Talagrand’s T₂ transportation cost-information inequality for the law of stochastic heat equation driven by Gaussian noise, which is fractional for a time variable with the Hurst index (H in ({1 over 2},1)), and is correlated for the spatial variable. The Girsanov theorem for fractional-colored Gaussian noise plays an important role in the proof.