共查询到20条相似文献,搜索用时 15 毫秒
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We find conditions under which measures belong to H−1(R2). Next we show that measures generated by the Prandtl, Kaden as well as Pullin spirals, objects considered by physicists as incompressible flows generating vorticity, satisfy assumptions of our theorem, thus they are (locally) elements of H−1(R2). Moreover, as a by-product, we prove an embedding of the space of Morrey type measures in H−1. 相似文献
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Armando V. Corro Antonio Martínez Keti Tenenblat 《Journal of Mathematical Analysis and Applications》2014
We consider Ribaucour transformations for flat surfaces in the hyperbolic 3-space, H3. We show that such transformations produce complete, embedded ends of horosphere type and curves of singularities which generically are cuspidal edges. Moreover, we prove that these ends and curves of singularities do not intersect. We apply Ribaucour transformations to rotational flat surfaces in H3 providing new families of explicitly given flat surfaces H3 which are determined by several parameters. For special choices of the parameters, we get surfaces that are periodic in one variable and surfaces with any even number or an infinite number of embedded ends of horosphere type. 相似文献
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We prove that the periodic modified Benjamin–Ono equation is locally well-posed in the energy space H1/2. This ensures the global well-posedness in the defocusing case. The proof is based on an Xs,b analysis of the system after a gauge transform. 相似文献
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We prove that the solution map of the two-component Camassa–Holm system is not uniformly continuous as a map from a bounded subset of the Sobolev space Hs(T)×Hr(T) to C([0,1],Hs(T)×Hr(T)) when s?1 and r?0. We also demonstrate the nonuniform continuous property in the continuous function space C1(T)×C1(T). 相似文献
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In this paper we prove a family of inequalities for differential forms in Heisenberg groups H1 and H2, that are the natural counterpart of a class of div–curl inequalities in de Rham?s complex proved by Lanzani & Stein and Bourgain & Brezis. 相似文献
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We prove that if for the curved n-body problem the masses are given, the minimum distance between the point masses of a specific type of relative equilibrium solution to that problem has a universal lower bound that is not equal to zero. We furthermore prove that the set of all such relative equilibria is compact. This class of relative equilibria includes all relative equilibria of the curved n -body problem in H2 and a significant subset of the relative equilibria for S2, S3 and H3. 相似文献
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This article concerns the time growth of Sobolev norms of classical solutions to the 3D quasi-linear wave equations with the null condition. Given initial data in Hs×Hs−1 with compact supports, the global well-posedness theory has been established independently by Klainerman [13] and Christodoulou [3], respectively, for a relatively large integer s . However, the highest order Sobolev energy, namely, the Hs energy of solutions may have a logarithmic growth in time. In this paper, we show that the Hs energy of solutions is also uniformly bounded for s?5. The proof employs the generalized energy method of Klainerman, enhanced by weighted L2 estimates and the ghost weight introduced by Alinhac. 相似文献
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Ferruccio Colombini Daniele Del Santo Francesco Fanelli Guy Métivier 《Journal de Mathématiques Pures et Appliquées》2013
In this paper we prove an energy estimate with no loss of derivatives for a strictly hyperbolic operator with Zygmund continuous second order coefficients both in time and in space. In particular, this estimate implies the well-posedness for the related Cauchy problem. On the one hand, this result is quite surprising, because it allows to consider coefficients which are not Lipschitz continuous in time. On the other hand, it holds true only in the very special case of initial data in H1/2×H−1/2. Paradifferential calculus with parameters is the main ingredient to the proof. 相似文献
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We describe the orbit space of the action of the group Sp(2)Sp(1) on the real Grassmann manifolds Grk(H2) in terms of certain quaternionic matrices of Moore rank not larger than 2. We then give a complete classification of valuations on the quaternionic plane H2 which are invariant under the action of the group Sp(2)Sp(1). 相似文献
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José A. Gálvez Antonio Martínez José L. Teruel 《Journal of Mathematical Analysis and Applications》2014
The paper deals with the study of complete embedded flat surfaces in H3 with a finite number of isolated singularities. We give a detailed information about its topology, conformal type and metric properties. We show how to solve the generalized Weyl?s problem of realizing isometrically any complete flat metric with Euclidean singularities in H3 which gives the existence of complete embedded flat surfaces with a finite arbitrary number of isolated singularities. 相似文献
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The purpose of this paper is to study a class of quotient modules of the Hardy module H2(Dn). Along with the two variables quotient modules introduced by W. Rudin, we introduce and study a large class of quotient modules, namely Rudin's quotient modules of H2(Dn). By exploiting the structure of minimal representations we obtain an explicit co-rank formula for Rudin's quotient modules. 相似文献
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Consider the semilinear wave equations in dimension 3 with a defocusing and superconformal power-type nonlinearity and with data lying in the Hs×Hs−1 (s<1) closure of smooth functions that are compactly supported inside a ball with fixed radius. We establish new bounds of the Sobolev norms of the solution. In particular, we prove that the Hs norm of the high frequency component of the solution grows like T∼(1−s)2+ in a neighborhood of s=1. In order to do that, we perform an analysis in a neighborhood of the cone, using the finite speed of propagation, an almost Shatah–Struwe estimate [17], an almost conservation law and a low–high frequency decomposition and .1 相似文献
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In this paper we consider the motion of a rigid body in a viscous incompressible fluid when some Navier slip conditions are prescribed on the body's boundary. The whole system “viscous incompressible fluid + rigid body” is assumed to occupy the full space R3. We start by proving the existence of global weak solutions to the Cauchy problem. Then, we exhibit several properties of these solutions. First, we show that the added-mass effect can be computed which yields better-than-expected regularity (in time) of the solid velocity-field. More precisely we prove that the solid translation and rotation velocities are in the Sobolev space H1. Second, we show that the case with the body fixed can be thought as the limit of infinite inertia of this system, that is when the solid density is multiplied by a factor converging to +∞. Finally we prove the convergence in the energy space of weak solutions “à la Leray” to smooth solutions of the system “inviscid incompressible fluid + rigid body” as the viscosity goes to zero, till the lifetime T of the smooth solution of the inviscid system. Moreover we show that the rate of convergence is optimal with respect to the viscosity and that the solid translation and rotation velocities converge in H1(0,T). 相似文献
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In this paper, the linear conforming finite element method for the one-dimensional Bérenger's PML boundary is investigated and well-posedness of the given equation is discussed. Furthermore, optimal error estimates and stability in the L2 or H1-norm are derived under the assumption that h, h2ω2 and h2ω3 are sufficiently small, where h is the mesh size and ω denotes a fixed frequency. Numerical examples are presented to validate the theoretical error bounds. 相似文献