Mathematische Nachrichten最新文献

In order to well understand the behavior of the Riemann zeta function inside the critical strip, we show, among other things, the Fourier expansion of the $��{\zeta }^k��\left(�s�\right)��$ ($��k�\in �N�$) in the half-plane $��\Re �s�>�1�/�2�$ and we deduce a necessary and sufficient condition for the truth of the Lindelöf hypothesis. Moreover, if $�{\Delta }_k$ denotes the error term in the Piltz divisor problem then for almost all $��x�\ge �1�$ and any given $��k�\in �N�$ we have

The paper deals with a family of evolution problems arising in the physical modeling of small amplitude acoustic phenomena occurring in a fluid, bounded by a surface of extended reaction. They are all derived in a Lagrangian framework. We study well-posedness of these problems, their mutual relations, and their relations with other evolution problems modeling the same physical phenomena. They are those introduced in an Eulerian framework and those which deal with the (standard in Theoretical Acoustics) velocity potential. The latter reduce to the well-known wave equation with acoustic boundary conditions. Finally, we prove that all problems are asymptotically stable provided the system is linearly damped.

We consider a class of physically relevant one-dimensional isentropic compressible Navier–Stokes equations with viscoelastic constitutive law of Oldroyd type. By establishing uniform a priori estimates (with respect to relaxation time), we show global existence of smooth solutions with small initial data. Moreover, we get global-in-time convergence of the system toward the classical isentropic compressible Navier–Stokes equations.

Given a Hermitian holomorphic vector bundle over a complex manifold, consider its flag bundles with the associated universal vector bundles endowed with the induced metrics. We prove that the universal formula for the push-forward of a polynomial in the Chern classes of all the possible universal vector bundles also holds pointwise at the level of Chern forms. A key step in our proof is the explicit computation, at a point of any flag bundle, of the Chern curvature of the universal vector bundles with the induced metrics. As an application, we provide an alternative version of the Jacobi–Trudi identity at the level of differential forms. We also show the positivity of a family of polynomials in the Chern forms of Griffiths semipositive vector bundles. This latter result partially confirms the Griffiths' conjecture on positive characteristic forms, which has raised considerable interest in recent years.

Systems of the first-order partial differential equations with singular solutions appear in many multiphysics problems and the weak formulation of the solution involves, in many cases, the product of distributions. In this paper, we study such a system derived from Eulerian droplet model for air particle flow. This is a $��2�\times ��2�$ non-strictly hyperbolic system of conservation laws with linear damping. We first study a regularized viscous system with variable viscosity term, obtain a weak asymptotic solution with general initial data and also get the solution in Colombeau algebra. We study the vanishing viscosity limit and show that this limit is a distributional solution. Further, we study the large-time asymptotic behavior of the viscous system. This important system is not very well studied due to complexities in the analysis. As far as we know, the only work done on this system is for Riemann type of initial data. The significance of this paper is that we work on the system having general initial data and not just initial data of the Riemann type.

In this paper, we discuss the boundedness of generalized fractional integral operators $�I_{�\rho �,�\tau �}$ on Musielak–Orlicz–Morrey spaces of an integral form $��L^{�\Phi �,�\omega �,�{\theta }_1�}��\left(�X�\right)��$ over bounded non-doubling metric measure spaces $�X$, where both $�\rho$ and $�\omega$ depend on $��x�\in �X�$. As an application, we give Sobolev-type inequalities for multiphase functions

We study the Dirichlet problem for the pseudoparabolic equation perturbed with the $��p�\left[�u�\right]�$-Laplacian diffusion term,