Author
Nader Masmoudi
Other affiliations: York University, New York University, École Normale Supérieure ...read more
Bio: Nader Masmoudi is an academic researcher from Courant Institute of Mathematical Sciences. The author has contributed to research in topics: Nonlinear system & Euler equations. The author has an hindex of 62, co-authored 245 publications receiving 10507 citations. Previous affiliations of Nader Masmoudi include York University & New York University.
Papers published on a yearly basis
Papers
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TL;DR: Various asymptotic results concerning global (weak) solutions of compressible isentropic Navier-Stokes equations are proved, establishing the convergence, as the density becomes constant and the Mach number goes to 0, towards solutions of incompressible models.
373 citations
TL;DR: In this article, the existence of global solutions for the gravity water wave equation in dimension 3, in the case of small data, was proved by combining energy estimates which yield control of L 2 related norms with dispersive estimates, which give decay in L 8.
Abstract: We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L 2 related norms, with dispersive estimates, which give decay in L 8 . To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.
358 citations
TL;DR: In this article, the authors analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R 2 and show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates.
Abstract: We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.
283 citations
TL;DR: It is proved existence and uniqueness of local and global solutions for a system of equations concerning an incompressible viscoelastic fluid of the Oldroyd type and a new a priori estimate for the two-dimensional Navier-Stokes system.
Abstract: We prove existence and uniqueness of local and global solutions for a system of equations concerning an incompressible viscoelastic fluid of the Oldroyd type. We also show a new a priori estimate f...
260 citations
TL;DR: In this paper, the authors considered a strong coupling between incompressible Navier-Stokes equations and some transport equations and proved that there exist global weak solutions for general initial conditions.
Abstract: The authors consider here some Oldroyd models of non-Newtonian flows consisting of a strong coupling between incompressible Navier-Stokes equations and some transport equations. It is proved that there exist global weak solutions for general initial conditions. The existence proof relies upon showing the propagation in time of the compactness of solutions.
251 citations
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Journal Article•
28,685 citations
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TL;DR: In this paper, a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) is presented.
Abstract: Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These
9,929 citations
01 Jan 1998
TL;DR: In this paper, the authors explore questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties, using diffusion processes as a model of a Markov process with continuous sample paths.
Abstract: We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.
2,446 citations
08 Jun 2006
TL;DR: In this paper, the Korteweg de Vries equation was used for ground state construction in the context of semilinear dispersive equations and wave maps from harmonic analysis.
Abstract: Ordinary differential equations Constant coefficient linear dispersive equations Semilinear dispersive equations The Korteweg de Vries equation Energy-critical semilinear dispersive equations Wave maps Tools from harmonic analysis Construction of ground states Bibliography.
1,733 citations