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Keywords
(1)
global well posedness
Related Publications
(12)
Global wellposedness for KdV in Sobolev Spaces of negative index
Almost conservat...
Global solutions...
Sharp Global wellposedness for KdV and modified KdV on R and T
Re nements of Strichartz inequality and applications to 2D NLS with critical nonlinearity
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A Refined Global WellPosedness Result for Schrödinger Equations with Derivative
A Refined Global WellPosedness Result for Schrödinger Equations with Derivative,10.1137/S0036141001394541,J. Colliander,M. Keel,G. Staffilani,H. Tak
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A Refined Global WellPosedness Result for Schrödinger Equations with Derivative
(
Citations: 40
)
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J. Colliander
,
M. Keel
,
G. Staffilani
,
H. Takaoka
,
T. Tao
Published in 2002.
DOI:
10.1137/S0036141001394541
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Citation Context
(25)
...We introduce as in [
1
], a radial
C
^{∞}
, monotone multiplier, taking values in [0, 1], where: and we define
I
:
H
^{ s }
→
H
^{1}
by
Daniela De Silva
,
et al.
Correction to “Global WellPosedness and Polynomial Bounds for the Def...
...Strichartz estimate, see, for example, [6,
13
, 28, 43],...
Dirk Hundertmark
,
et al.
On nonlocal variational problems with lack of compactness related to ...
...Proof of Lemma 3. This result is known to the experts, see, for example [
8
,28]...
...for some constant depending on d, see, for example, [15,
8
]...
Dirk Hundertmark
,
et al.
Decay Estimates and Smoothness for Solutions of the Dispersion Managed...
...Existence of global solutions to (1.1)(1.2) corresponding to initial data below the energy treshold was first obtained in [6], [
7
] by using the method of “almost conservation laws”, or “Imethod” (for a detailed description of this method see section 3 below)...
...[1]) along with Strichartz estimates, to demonstrate the existence of global rough solutions (see [6,
7
] and [21])...
...4 We use the second modified energy approach as in [
7
] and [21]...
Daniela De Silva
,
et al.
Global WellPosedness and Polynomial Bounds for the Defocusing L Criti...
...We have the following basic cancellation bound (cf. [
6
]):...
Michael Christ
,
et al.
A priori bounds and weak solutions for the nonlinear Schrödinger equat...
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Journal:
Selecta Mathematicanew Series  SEL MATHNEW SER
, vol. 3, no. 2, pp. 115159, 1997
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Citations
(40)
On Nonlocal Variational Problems with Lack of Compactness Related to Nonlinear Optics
Dirk Hundertmark
,
YoungRan Lee
Journal:
Journal of Nonlinear Science  J NONLINEAR SCI
, pp. 138, 2011
Global rough solutions to the critical generalized KdV equation
(
Citations: 3
)
Luiz Gustavo Farah
Journal:
Journal of Differential Equations  J DIFFERENTIAL EQUATIONS
, vol. 249, no. 8, pp. 19681985, 2010
Global rough solutions to the cubic nonlinear Boussinesq equation
(
Citations: 1
)
Luiz Gustavo Farah
,
Felipe Linares
Journal:
Journal of The London Mathematical Societysecond Series  J LONDON MATH SOCSECOND SER
, vol. 81, no. 1, pp. 241254, 2010
Exponential decay of dispersion managed solitons for vanishing average dispersion
(
Citations: 2
)
M. Burak Erdogan
,
Dirk Hundertmark
,
YoungRan Lee
Published in 2010.
Correction to “Global WellPosedness and Polynomial Bounds for the Defocusing L Critical Nonlinear Schrödinger Equation in ℝ”
Daniela De Silva
,
Gigliola Staffilani
,
Nikolaos Tzirakis
Journal:
Communications in Partial Differential Equations  COMMUN PART DIFF EQUAT
, vol. 36, no. 2, pp. 293303, 2010