共查询到20条相似文献,搜索用时 85 毫秒
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This paper studies the asymptotic behavior of smooth solutions to the generalized Hall-magneto-hydrodynamics system (1.1) with one single diffusion on the whole space . We establish that, in the inviscid resistive case, the energy vanishes and converges to a constant as time tends to infinity provided the velocity is bounded in ; in the viscous non-resistive case, the energy vanishes and converges to a constant provided the magnetic field is bounded in . In summary, one single diffusion, being as weak as or with small enough , is sufficient to prevent asymptotic energy oscillations for certain smooth solutions to the system. 相似文献
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We study the non-linear minimization problem on with , and : where presents a global minimum α at with . In order to describe the concentration of around , one needs to calibrate the behavior of with respect to s. The model case is In a previous paper dedicated to the same problem with , we showed that minimizers exist only in the range , which corresponds to a dominant non-linear term. On the contrary, the linear influence for prevented their existence. The goal of this present paper is to show that for , and , minimizers do exist. 相似文献
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Riccardo Adami Ugo Boscain Valentina Franceschi Dario Prandi 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2021,38(4):1095-1113
In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on is essentially self-adjoint in . A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on is never essentially self-adjoint in , if . We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass. 相似文献
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We investigate a sharp Moser–Trudinger inequality which involves the anisotropic Dirichlet norm on for . Here F is convex and homogeneous of degree 1, and its polar represents a Finsler metric on . Under this anisotropic Dirichlet norm, we establish the Lions type concentration-compactness alternative. Then by using a blow-up procedure, we obtain the existence of extremal functions for this sharp geometric inequality. 相似文献
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This paper discusses the quasilinear Schrödinger equation where . Under appropriate assumptions on the potentials and and local sublinear growth assumptions on the nonlinear term , we get the existence of infinitely many nontrivial solutions by using a revised Clark theorem and a priori estimate of the solution. 相似文献
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《Indagationes Mathematicae》2022,33(2):322-333
We apply the techniques developed by I. Panin for the proof of the equicharacteristic case of the Serre–Grothendieck conjecture for isotropic reductive groups (Panin et al., 2015; Panin, 2019) to obtain similar injectivity and -invariance theorems for non-stable -functors associated to isotropic reductive groups. Namely, let be a reductive group over a commutative ring . We say that has isotropic rank , if every non-trivial normal semisimple -subgroup of contains . We show that if has isotropic rank and is a regular domain containing a field, then , where is the corresponding non-stable -functor, also called the Whitehead group of . If is, moreover, local, then we show that is injective, where is the field of fractions of . 相似文献
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This paper is concerned with a gauged nonlinear Schrödinger equation Under some suitable conditions on the nonlinearity , we obtain two new existence results of infinitely many high energy solutions by using variational methods, and our results generalize and improve the recent result in the literature. 相似文献
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Eduard Curcă 《Comptes Rendus Mathematique》2019,357(4):355-359
Let . If has zero integral, then the equation need not have a solution [6] or even [2]. Using these results, we prove that, whenever and , there exists some ?-form such that and the equation has no solution . This provides a negative answer to a question raised by Baldi, Franchi, and Pansu [1]. 相似文献
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A new a priori estimate for solutions to Navier–Stokes equations is derived. Uniqueness and existence of these solutions in for all is proved in a class of solutions locally differentiable in time with values in , where is the Sobolev space. By the solution a solution to an integral equation is understood. No smallness restrictions on the data are imposed. 相似文献
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Luigi Ambrosio Shouhei Honda Jacobus W. Portegies David Tewodrose 《Journal of Functional Analysis》2021,280(10):108968
In this paper we study the family of embeddings of a compact space into via eigenmaps. Extending part of the classical results [10], [11] known for closed Riemannian manifolds, we prove convergence as of the rescaled pull-back metrics in induced by . Moreover we discuss the behavior of with respect to measured Gromov-Hausdorff convergence and t. Applications include the quantitative -convergence in the noncollapsed setting for all , a result new even for closed Riemannian manifolds and Alexandrov spaces. 相似文献
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We are concerned with magneto-micropolar fluid equations (1.3)–(1.4). The global existence of solutions to the Cauchy problem is investigated under certain conditions. Precisely, for the magneto-micropolar-Navier–Stokes (MMNS) system, we obtain global existence and large time behavior of solutions near a constant states in . Appealing to a refined pure energy method, we first obtain a global existence theorem by assuming that the norm of the initial data is small, but the higher order derivatives can be arbitrary large. If the initial data belongs to homogeneous Sobolev norms or homogeneous Besov norms , we obtain the optimal decay rates of the solutions and its higher order derivatives. As an immediate byproduct, we also obtain the usual type of the decay rates without requiring that the norm of initial data is small. At last, we derive a weak solution to (1.3)–(1.4) in with large initial data. 相似文献
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In this paper, we completely determine all necessary and sufficient conditions such that the polynomial , where , is a permutation quadrinomial of over any finite field of odd characteristic. This quadrinomial has been studied first in [25] by Tu, Zeng and Helleseth, later in [24] Tu, Liu and Zeng revisited these quadrinomials and they proposed a more comprehensive characterization of the coefficients that results with new permutation quadrinomials, where and finally, in [16], Li, Qu, Li and Chen proved that the sufficient condition given in [24] is also necessary and thus completed the solution in even characteristic case. In [6] Gupta studied the permutation properties of the polynomial , where and and proposed some new classes of permutation quadrinomials of .In particular, in this paper we classify all permutation polynomials of of the form , where , over all finite fields of odd characteristic and obtain several new classes of such permutation quadrinomials. 相似文献