Results 11 to 20 of about 2,675,517 (69)
A remark on normal forms and the "upside-down" I-method for periodic NLS: growth of higher Sobolev norms [PDF]
, 2011 We study growth of higher Sobolev norms of solutions to the one-dimensional periodic nonlinear Schrodinger equation (NLS). By a combination of the normal form reduction and the upside-down I-method, we establish \|u(t)\|_{H^s} \lesssim (1+|t|)^{\alpha (s-
Colliander, James +2 more
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Complex plane representations and stationary states in cubic and quintic resonant systems
, 2019 Weakly nonlinear energy transfer between normal modes of strongly resonant PDEs is captured by the corresponding effective resonant systems. In a previous article, we have constructed a large class of such resonant systems (with specific representatives ...
Biasi, Anxo, Bizon, Piotr, Evnin, Oleg
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Solvable cubic resonant systems
, 2019 Weakly nonlinear analysis of resonant PDEs in recent literature has generated a number of resonant systems for slow evolution of the normal mode amplitudes that possess remarkable properties.
Biasi, Anxo, Bizon, Piotr, Evnin, Oleg
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Exponential decay properties of a mathematical model for a certain fluid-structure interaction
, 2014 In this work, we derive a result of exponential stability for a coupled system of partial differential equations (PDEs) which governs a certain fluid-structure interaction.
Avalos, George, Bucci, Francesca
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Local well-posedness and singularity formation in non-Newtonian compressible fluids
, 2023 We investigate the initial value problem of a very general class of $3+1$ non-Newtonian compressible fluids in which the viscous stress tensor with shear and bulk viscosity relaxes to its Navier-Stokes values.
Disconzi, Marcelo M. +2 more
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, 2012 Two unusual time-integral conditional regularity results are presented for the three-dimensional Navier-Stokes equations. The ideas are based on $L^{2m}$-norms of the vorticity, denoted by $\Omega_{m}(t)$, and particularly on $D_{m} = \Omega_{m}^{\alpha_{
Constantin P. +9 more
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On the probabilistic Cauchy theory for nonlinear dispersive PDEs
, 2018 In this note, we review some of the recent developments in the well-posedness theory of nonlinear dispersive partial differential equations with random initial data.Comment: 26 pages. To appear in Landscapes of Time-Frequency Analysis, Appl.
A Choffrut +45 more
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A remark on randomization of a general function of negative regularity
, 2023 In the study of partial differential equations (PDEs) with random initial data and singular stochastic PDEs with random forcing, we typically decompose a classically ill-defined solution map into two steps, where, in the first step, we use stochastic ...
Oh, Tadahiro +3 more
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Conformal flow on $S^3$ and weak field integrability in AdS$_4$
, 2017 We consider the conformally invariant cubic wave equation on the Einstein cylinder $\mathbb{R} \times \mathbb{S}^3$ for small rotationally symmetric initial data.
Bizoń, Piotr +5 more
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Recent results in mathematical relativity
, 2004 We review selected recent results concerning the global structure of solutions of the vacuum Einstein equations. The topics covered include quasi-local mass, strong cosmic censorship, non-linear stability, new constructions of solutions of the constraint
Chrusciel, Piotr T.
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