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Interior regularity of weak solutions to the perturbed Navier-Stokes equations

Pigong Han (2012)

Applications of Mathematics

In this paper we establish interior regularity for weak solutions and partial regularity for suitable weak solutions of the perturbed Navier-Stokes system, which can be regarded as generalizations of the results in L. Caffarelli, R. Kohn, L. Nirenberg: Partial regularity of suitable weak solutions of the Navier-Stokes equations, Commun. Pure. Appl. Math. 35 (1982), 771–831, and S. Takahashi, On interior regularity criteria for weak solutions of the Navier-Stokes equations, Manuscr. Math. 69...

Invariant measures and long-time behavior for the Benjamin-Ono equation

Yu Deng, Nikolay Tzvetkov, Nicola Visciglia (2014)

Journées Équations aux dérivées partielles

We summarize the main ideas in a series of papers ([20], [21], [22], [5]) devoted to the construction of invariant measures and to the long-time behavior of solutions of the periodic Benjamin-Ono equation.

Invertibility of some heat potentials in $B M O$ norms

Anna Grimaldi-Piro, Francesco Ragnedda, Umberto Neri (1986)

Rendiconti del Seminario Matematico della Università di Padova

Isoperimetric inequalities in parabolic equations

J. Mossino, J. M. Rakotoson (1986)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Kolmogorov Diameters in Solution Spaces of Systems of Partial Differential Equations.

Michael Langenbruch (1985)

Manuscripta mathematica

$L_{p}$ -oценки решения задачи Коши для одномерного гиперболического уравнения высокого порядка с постоянными коэффициентами

Ю.И. Балтаг (1987)

Matematiceskie issledovanija

$L_{p}$ -regularity of solutions to first initial-boundary value problem for hyperbolic equations in cusp domains.

Nguyen Manh Hung, Vu Trong Luong (2009)

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

$L^{p}$ regularity of velocity averages

R. J. Diperna, P. L. Lions, Y. Meyer (1991)

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

L2-Integrability of Second Order Derivatives for Poisson's Equation in Nonsmooth Domains.

Vilhelm Adolfsson (1992)

Mathematica Scandinavica

Le problème de la dérivée oblique non linéaire

Paul Godin (1983)

Journées équations aux dérivées partielles

L'equazione $\Delta_{2}u+a_{10}(x,y)\frac{\partial u}{\partial x}+a_{01}(x,y)\frac{\partial u% }{\partial y}+a_{00}(x,y)u=F(x,y)$ . Teorema di esistenza per un generale problema al contorno

Alberto Cialdea (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Necessary and sufficient conditions are given for the existence of smooth solutions of the differential equations (1) with the boundary conditions (2). Coefficients of (1) and (2) are only supposed Hölder-continuous.

Les théorèmes de Leray et de Fujita-Kato pour le système de Boussinesq partiellement visqueux

Raphaël Danchin, Marius Paicu (2008)

Bulletin de la Société Mathématique de France

Dans cet article, on étudie le système de Boussinesq décrivant le phénomène de convection dans un fluide incompressible et visqueux. Ce système est composé des équations de Navier-Stokes incompressibles avec un terme de force verticale dont l’amplitude est transportée sans dissipationpar le flot du champ de vitesses. On montre que les résultats classiques pour le système de Navier-Stokes standard demeurent vrais pour le système de Boussinesq bien qu’il n’y ait pas d’amortissement sur le terme de...

Levi equation for almost complex structures.

Giovanna Citti, Giuseppe Tomassini (2004)

Revista Matemática Iberoamericana

Linear Oblique Derivative Problems for the Uniformly Elliptic Hamilton-Jacobi-Bellman Equation.

P.-L. Lions, N.S. Trudinger (1986)

Mathematische Zeitschrift

Line-energy Ginzburg-Landau models : zero-energy states

Pierre-Emmanuel Jabin, Felix Otto, BenoÎt Perthame (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We consider a class of two-dimensional Ginzburg-Landau problems which are characterized by energy density concentrations on a one-dimensional set. In this paper, we investigate the states of vanishing energy. We classify these zero-energy states in the whole space: They are either constant or a vortex. A bounded domain can sustain a zero-energy state only if the domain is a disk and the state a vortex. Our proof is based on specific entropies which lead to a kinetic formulation, and on a careful...