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Mixed dimensional infinite soliton trains for nonlinear Schrödinger equations
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Liouville theorems for stable solutions of the weighted Lane-Emden system
Discrete Schrödinger equation and ill-posedness for the Euler equation
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$U(x,y) = \left( {\begin{array}{*{20}{c}}{\cos \;y}\\0\end{array}} \right)$ |
References:
[1] |
J. Bourgain and D. Li,
Strong Ill-posedness of the incompressible Euler equation inborderline Sobolev spaces, Invent. Math., 20 (2015), 97-157.
doi: 10.1007/s00222-014-0548-6. |
[2] |
J. Bourgain and D. Li,
Strong illposedness of the incompressible Euler equation in integer $C^m$ spaces, Geom. Funct. Anal., 25 (2015), 1-86.
doi: 10.1007/s00039-015-0311-1. |
[3] |
A. Cheskidov and R. Shvydkoy,
Ill-posedness of the basic equations of fluid dynamics in Besov spaces, Proceedings of AMS, 138 (2010), 1059-1067.
doi: 10.1090/S0002-9939-09-10141-7. |
[4] |
D. Ebin and J. Marsden,
Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. Math., 92 (1970), 102-163.
doi: 10.2307/1970699. |
[5] |
T. Elgindi and N. Masmoudi, L∞ Ill-posedness for a class of equations arising in hydrodynamics, preprint, arXiv: 1405.2478v2. |
[6] |
A. Grünrock and S. Herr,
Low regularity local well-posedness of the derivative nonlinear Schrödinger equation with periodic initial data, SIAM Journal on Mathematical Analysis, 39 (2008), 1890-1920.
doi: 10.1137/070689139. |
[7] |
T. Kato,
Nonstationary flows of viscous and ideal fluids in $\mathbb{R}^3$, J. Func. Anal., 9 (1972), 296-305.
doi: 10.1016/0022-1236(72)90003-1. |
[8] |
T. Kato,
The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Ration. Mech. Anal., 58 (1975), 181-205.
doi: 10.1007/BF00280740. |
[9] |
J. Mattingly and Ya. Sinai,
An elementary proof of the existence and uniqueness theorem for the Navier-Stokes equations, Commun. Contemp. Math., 1 (1999), 497-516.
doi: 10.1142/S0219199799000183. |
show all references
References:
[1] |
J. Bourgain and D. Li,
Strong Ill-posedness of the incompressible Euler equation inborderline Sobolev spaces, Invent. Math., 20 (2015), 97-157.
doi: 10.1007/s00222-014-0548-6. |
[2] |
J. Bourgain and D. Li,
Strong illposedness of the incompressible Euler equation in integer $C^m$ spaces, Geom. Funct. Anal., 25 (2015), 1-86.
doi: 10.1007/s00039-015-0311-1. |
[3] |
A. Cheskidov and R. Shvydkoy,
Ill-posedness of the basic equations of fluid dynamics in Besov spaces, Proceedings of AMS, 138 (2010), 1059-1067.
doi: 10.1090/S0002-9939-09-10141-7. |
[4] |
D. Ebin and J. Marsden,
Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. Math., 92 (1970), 102-163.
doi: 10.2307/1970699. |
[5] |
T. Elgindi and N. Masmoudi, L∞ Ill-posedness for a class of equations arising in hydrodynamics, preprint, arXiv: 1405.2478v2. |
[6] |
A. Grünrock and S. Herr,
Low regularity local well-posedness of the derivative nonlinear Schrödinger equation with periodic initial data, SIAM Journal on Mathematical Analysis, 39 (2008), 1890-1920.
doi: 10.1137/070689139. |
[7] |
T. Kato,
Nonstationary flows of viscous and ideal fluids in $\mathbb{R}^3$, J. Func. Anal., 9 (1972), 296-305.
doi: 10.1016/0022-1236(72)90003-1. |
[8] |
T. Kato,
The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Ration. Mech. Anal., 58 (1975), 181-205.
doi: 10.1007/BF00280740. |
[9] |
J. Mattingly and Ya. Sinai,
An elementary proof of the existence and uniqueness theorem for the Navier-Stokes equations, Commun. Contemp. Math., 1 (1999), 497-516.
doi: 10.1142/S0219199799000183. |
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