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We consider the 3D quantum BBGKY hierarchy which corresponds to the $N$ -particle Schrödinger equation. We assume the pair interaction is $N^{3 β - 1} V (B^{β})$ . For the interaction parameter $β \in (0, 2 / 3)$ , we prove that, provided an energy bound holds for solutions to the BBKGY hierarchy, the $N \to \infty$ limit points satisfy the space-time bound conjectured by S. Klainerman and M. Machedon [45] in 2008. The energy bound was proven to hold for $β \in (0, 3 / 5)$ in [28]. This allows, in the case $β \in (0, 3 / 5)$ , for the application of the Klainerman–Machedon uniqueness theorem...

On the local behaviour of solutions of a certain class of doubly nonlinear parabolic equations.

Vincenzo Vespri (1992)

Manuscripta mathematica

On the long-time behaviour of solutions of the p-Laplacian parabolic system

Paweł Goldstein (2008)

Colloquium Mathematicae

Convergence of global solutions to stationary solutions for a class of degenerate parabolic systems related to the p-Laplacian operator is proved. A similar result is obtained for a variable exponent p. In the case of p constant, the convergence is proved to be $¹_{l o c}$ , and in the variable exponent case, L² and $W^{1, p (x)}$ -weak.

On the optimality of velocity averaging lemmas

Camillo de Lellis, Michael Westdickenberg (2003)

Annales de l'I.H.P. Analyse non linéaire

On the parameter dependence of solutions to the ...-equation.

Takeo Ohsawa, Klaus Diederich (1991)

Mathematische Annalen

On the Partial Regularity of Weak Solutions of Nonlinear Parabolic Systems.

Michael Struwe, Mariano Giaquinta (1982)

Mathematische Zeitschrift

On the precise asymptotics of the constant in Friedrich's inequality for functions vanishing on the part of the boundary with microinhomogeneous structure.

Chechkin, G.A., Koroleva, Yu.O., Persson, L.-E. (2007)

Journal of Inequalities and Applications [electronic only]

On the rate of the volume growth for symmetric viscous heat-conducting gas flows with a free boundary.

Zlotnik, Alexander (2006)

Abstract and Applied Analysis

On the regularity of averages over spheres for kinetic transport equations in hyperbolic Sobolev spaces.

N. Bournaveas, S. Gutiérrez (2007)

Revista Matemática Iberoamericana

On the rigidity of minimal mass solutions to the focusing mass-critical NLS for rough initial data.

Li, Dong, Zhang, Xiaoyi (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

On the Schauder estimates of solutions to parabolic equations

Qing Han (1998)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On the Schrödinger equation in L...spaces.

O. El-Mennaoui, V. Keyantuo (1996)

Mathematische Annalen

On the second order derivatives of convex functions on the Heisenberg group

Cristian E. Gutiérrez, Annamaria Montanari (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In the euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem states that convex functions are a.e. twice differentiable. In this paper we prove that a similar result holds in the Heisenberg group, by showing that every continuous $ℋ$ –convex function belongs to the class of functions whose second order horizontal distributional derivatives are Radon measures. Together with a recent result by Ambrosio and Magnani, this proves the existence a.e. of second order horizontal derivatives for...

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Displaying 61 – 80 of 96

On the existence of a fundamental solution for a parabolic differential equation with unbounded coefficients

On the Fejér-F. Riesz inequality in $L^{p}$

On the global well-posedness of the Boussinesq system with zero viscosity

On the Klainerman–Machedon conjecture for the quantum BBGKY hierarchy with self-interaction