# sw NLPDE Z~i[

## 2013Nx̃Z~i[̋L^

2013 N 4 19 ijj 15:30  17:30
sw w 3 251
u
qV iÉwȊwȁj
u
Uniqueness of steady Navier-Stokes flows in exterior domains
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{uł3ÖɂNavier-Stokes̉̈ӐɂāCɗ^ꂽ2̉̂1̉Ƃ͌Ȃꍇ̈Ӑl@D ʂɊ҂łŗǌƂ炦悤Ȏ$L^p$Ԃ̘gg݂𓱓邱Ƃ3Ỏ𐫂Kozono-Yamazaki('98)̃NX̉lCۓStokes̉̐̕p邱ƂɂC2̉̂̈$L^3$ԂŏC̉$L^3 + L^{\infty}$ɑȂΈӐ藧ƂD

2013 N 4 26 ijj 15:30  17:30
sw w 3 251
u
m iswwȁj
u
Dynamics of topological defect in Bose-Einstein condensates with spin degrees of freedom
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1990N㔼ɎꂽC󔖌qC̃{[XÏk̂̃_Ci~NX́CVfBK[pĒʓIɗǂLqD ̏dvȃgsbNX1ƂėʎqQ̂悤ȃg|WJׂ̃_Ci~NXD ʏ̕f1̏ꍇɂׂ͐łʎqQ݂݂̂邪CXsRxXsmE{[XÏkɑ΂CfɊgꂽVfBK[ɂȂƁC̏̃g|WJȍ\𔽉fėlXȃg|WJׂ̃_Ci~NXD uł͂̒̋[ƂāC_ׂ̕_Ci~NXCpseudo-Nambu-Goldstone[hɂʎqQ̕_Ci~NXCQbladingяՓ˃_Ci~NXɂčuD

2013 N 5 10 ijj 15:30  16:30
sw w 3 251
u
Piero D'Ancona iDepartment of Mathematics, University of Rome I "La Sapienza"j
u
On the Helmholtz equation with long range variable coefficients on an exterior domain
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In a joint work with F. Cacciafesta and R. Luca', we prove global smoothing estimates for a Helmholtz equation with fully variable long range coefficients plus electromagnetic potentials on the exterior of a starshaped obstacle, with Dirichlet boundary conditions. Natural applications are to weak dispersion for Schrödinger and wave equations with variable coefficients.

2013 N 5 17 ijj 15:30  17:30
sw w 3 251
u
R _V iÉwȊwȁj
u
Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations at the scaling critical regularity
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{uł1K̔܂2̔^VfBK[̘An̏lɂčlD PƂ̏̕ꍇɂ͔^ɂ̑̂߁Cʂɂ͒ʏ̃\{tH^{s}ɂKؐ𓱂Ƃ͂łȂD CAnŃvVǍW𖞂ꍇɂ͉̑񕜂邱ƂłC\{tԂɂKؐ邱ƂD ɍ̏ꍇɂ́Ct[Gm𐸖U^2, V^2^̃mp邱ƂɂCXP[ՊEȃ\{tԂɂKؐ邱ƂD

2013 N 5 24 ijj 15:30  17:30
sw w 3 251
u
Oc itwwȁj
u
On the asymptotic stability of fast moving soliton
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3ɂ|eVtVfBK[NLSlD |eVƂNLSȊԉƉ肵CKCϊŐisgɕς̂̋߂lƂ|eVtNLS̉ǂ̂悤ɂӂ܂̂𒲂ׂD {uł͎ɐpf̘AXyNg̃Rg[ɕKvȃXgbJ[c]ɂĉD {uł̌ʂS.Cuccagna(Triestew)Ƃ̋ɊÂD

2013 N 5 31 ijj 15:30  17:30
sw w 3 251
u
Xiangdi Huang iwȊw/Ȋw@j
u
Serrin's criterion on various compressible models and its applications
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In this talk, blowup criteria for strong and classical solutions of the three dimensional compressible flows are considered. We extend the well known Serrin's regularity criterion for Navier-Stokes equations to various compressible models, from baratropic flow to viscous compressible and heat conducting magnetohydrodynamic flows. As an application, we will establish some existence of global solution for compressible flows with vacuum and large oscillations.

2013 N 6 7 ijj 15:30  17:30
sw w 3 251
u
Ԗx j iÉwHwȁj
u
Remarks on scattering problem for the energy-critical nonlinear Schrödinger equation
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GlM[ՊEVfBK[ɂčl@D ̕ɑ΂ẮCTalenti֐ƂȂĂāCGlM[Ɖ^GlM[͎RɎU鎖\zĂD ہCKenig-Merle(2006) Killip-Visan(2010) ɂāCꂼCΏ̉Ƌ5ȏ̏ꍇɍmIȌʂĂD ǂ̏ꍇؖ̌ƂȂ̂́Cminimal blowup solutionƌĂ΂łC݂̉̑ے肷鎖ɂďؖD ɁCKillip-Visan̏ؖł́Cfinite-time blowup, low-to-high frequency cascade, soliton-like3̃ViIɕčl@ĂD ǂ̎łCfinite-time blowup͂Ȃ邽߁C3,4̎ɁClow-to-high frequency cascadesoliton-like2̃ViIȂؖΗ\z邪CłD ̍uł́Clow-to-high frequency cascadȅꍇے肷邽߂ɗLƎvAv[ƁCsoliton-likȅꍇ̉͂ɖ𗧂ȕ"almost zero-momentum"ЉD

2013 N 6 14 ijj 15:30  17:30
sw w 3 251
u
G iwwȁj
u
Null structure in a system of quadratic derivative nonlinear Schrödinger equations
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This talk is based on a joint work with M.Ikeda and S.Katayama. We consider the initial value problem for a three-component system of quadratic derivative nonlinear Schrödinger equations in two space dimensions with the masses satisfying a resonance relation. We introduce a structural condition on the nonlinearity under which the solution is asymptotically free in the large time. Several related problems will be also discussed.

2013 N 6 21 ijj 15:30  17:30
sw w 3 251
u
⌳ ] iLwwȁj
u
Steklov-eigenvalue problems arising in diffusion systems under dynamic boundary conditions
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We consider N-component systems of diagonal diffusion equations under dynamic boundary conditions on bounded smooth domains. The features of our system are as follows.
1. Each component diffuses freely (independently from other components) inside the domain (there is no interaction in bulk);
2. There are dynamic interactions between the components involved on the boundary.
We are interested in the stability of trivial solutions of such a system, and the linearized problem is characterized by the diagonal diffusion matrix D (which acts in the interior of domain), together with the mass transfer and boundary rate matrices J and W, respectively, which act on the boundary. We emphasize that the matrices D and W have to be positive definite by nature. As regard to the linearized eigenvalue problem, we obtained the following results.
1. When J is symmetric, we obtained a variational characterization of all eigenvalues:
(a-1) All eigenvalues of our problem are real.
(a-2) If J is negative definite, then all eigenvalues of our problem are negative.
(a-3) If J has a positive eigenvalue, then our problem has corresponding positive eigenvalues.
1. When the diffusion matrix D and the boundary rate matrix are constant multiples of the N by N identity matrix, then we identified a smooth region U in the complex plane C for which we have:
(b-1) If all eigenvalues of J belong to the interior of U, then the eigenvalues of our problem have negative real part.
(b-2) If J has an eigenvalue belonging to the exterior of U, then our problem has a corresponding eigenvalue with positive real part.
(b-3) If J has an eigenvalue on the boundary of U, then our problem has a corresponding pure-imaginary eigenvalue.
One of the key ingredients to obtain these result is to formulate our problem in terms of Steklov-eigenvalue problems. This is a joint work with Ciprian Gal of Florida International University.

2013 N 7 12 ijj 16:00  17:30
sw w 3 251
u
Neal Bez iUniversity of Birminghamj
u
Sharp space-time estimates for dispersive PDE
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I will present some recent work on finding optimal constants and the existence/shape of maximising initial data for certain Strichartz and Kato-smoothing estimates.

2013 N 7 19 ijj 15:30  18:00
sw w 3 251
u
Nikolay Tzvetkov iUniversité de Cergy-Pontoisej
u
yPart Iz 15:30  16:30
On the long time behavior of the Benjamin-Ono equation
yPart IIz 17:00  18:00
Multi-solitons for the water-waves system
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yPart Iz The KdV and the Benjamin-Ono equations are basic models, derived from the water waves equations for the propagation of long, small amplitude one dimensional waves. The solutions of the KdV equations, posed on the torus are known to be almost periodic in time. The long time behavior of the Benjamin-Ono equation, posed on the torus is much less understood. In this talk, we will present some progress on this problem. Namely, we shall construct an infinite sequence of weighted gaussian measures which are invariant by the flow of the Benjamin-Ono equation. These measures are supported by Sobolev spaces of increasing regularities. The "probabilistic view point" is essential in our analysis. In particular our arguments are less dependent on the particular behavior of each trajectory, compared to previous works on the subject. The talk is based on a series of joint works with Nicola Visciglia.

yPart IIz We will present the construction of multi-solitons solutions (that is to say solutions that are time asymptotics to a sum of decoupling solitary waves) for the full water waves system with surface tension. This is a generalization of similar results obtained for strongly simplified model equations such as the KdV equation. The construction is quite different compared with the one solitons obtained in the classical work by Amick-Kirchgässner since one has a dispersive tail added to the main multi-soliton core. The talk is based on a joint work with Mei Ming and Frédéric Rousset.

2013 N 10 4 ijj 16:00  18:00
sw w 3 251
u
MV iswwȁj
u
Anomalous enstrophy dissipation in a point vortex system
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2013 N 10 11 ijj 15:30  17:30
sw w 3 251
u
c l iȑwwj
u
Instability of solitary waves for nonlinear Schrödinger equations of derivative type
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^VfBK[́CpUƕixƂ2̃p[^ɖ{IɈˑǗg̑D ̌Ǘg̋O萫ɂĂ͈ȑǑɂ蕪ĂD ́C1p[^̌Ǘgɑ΂Os萫Ɋւ]̕@C2p[^̏ꍇɊg邱ƂɂCʂ̃p[^̈ɂǗg̋Os萫D

2013 N 10 18 ijj 15:30  17:30
sw w 3 251
u
ᐙ E iwwȁj
u
On diffusion phenomena for the linear wave equation with space-dependent damping
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ԕϐɈˑ門CU^glD {uł́C̊gUہCȂ킿CԖɂđΉM̉ɑQ߂邱ƂD Todorova-Yordanov2009ŇʂɂāC̃GlM[̂قڍŗǂȌ]͓ĂC̑QߌɂĂ͖łD CTodorova-YordanovɂdݕtGlM[]CK̓֐ɂ܂Ŋĝp邱ƂɂCQߌ߂邱Ƃł̂ŁC񍐂D

2013 N 10 25 ijj 15:30  17:30
sw w 3 251
u
Oc itwwȁj
u
On small energy stabilization in the NLS with a trapping potential
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We describe the asymptotic behavior of small energy solutions of an NLS with a trapping potential. In particular we generalize work of Soffer and Weinstein, and of Tsai and Yau. The novelty is that we allow generic spectra associated to the potential. This is yet a new application of the idea to interpret the nonlinear Fermi Golden Rule as a consequence of the Hamiltonian structure. This is a joint work with Scipio Cuccagna (Trieste University).

2013 N 11 1 ijj 15:30  17:30
sw w 3 251
u
{{ l iwȊwȁj
u
\{tDՊE̔mC}̐lΏ̉̍\ɂ
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̈ɂ\{tDՊE̔Neumann ^2u-u+u^p=0 ̐lΏ̉̍\lD N (>=3) ԎƂƂC p \{tՊEw (N+2)/(N-2) 菬iՊEjCiՊEjC傫iDՊEjɉāC̍\傫ς邱ƂmĂD uł p 傫ꍇiDՊEj̐lΏ̉̍\i}jlD ՊEՊȄꍇ̉\Ɣr邱ƂɂāC\{t̖ߍ݂藧ȂɓĽۂTD

2013 N 11 8 ijj 15:30  17:30
sw w 3 251
u
V iÍHƍwZj
u
Spreading speed and profile for nonlinear diffusion problems with free boundaries
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1ԏ̔gU̎RElD PCoCRČ^ƌĂ΂3^Cv̂ꂩłꍇCԖɂڍׂȑQߋDuLouɂēꂽD ̓Iɂ͎Ɏ2̏ꍇNF
@(1) RE t ɂĐ̖ɔUC֐u͂鐳̒萔ɍLlispreadingjC
@(2) RE t ɂėL͈̔͂ɂƂǂ܂Cu0ɎivanishingjD
{uł͊֘ACauchyƐisgɊւsЉƁCDuLoǔɂāCspreadingNꍇCRE̐isxispreading speedj̏ڂ]ƁCԂ\o߂Ƃł͊֐û͔݂猈܂邠֐ɋ߂ÂƂD
{uYihong DuiUniversity of New England, AustraliajMaolin ZhouiwjƂ̋ɊÂD

2013 N 11 15 ijj 15:30  17:30
sw w 3 251
u
a Iq iw|wwj
u
Finite-time blowup in the two-dimensional parabolic Keller-Segel system
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2013 N 11 22 ijj 15:30  17:30
sw w 3 251
u
gc ĊC iwȊwȁj
u
Asymptotic behavior of solutions toward a multiwave pattern for the scalar conservation law with degenerate flux and viscosity
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We study the asymptotic behavior of solutions toward a multiwave pattern (rarefaction wave and viscous contact wave) of the Cauchy problem for one-dimensional viscous conservation law where the far field states are prescribed. Especially, we deal with the case when the flux function is convex or concave but linearly degenerate on some interval, and also the viscosity is a nonlinearly degenerate one. The most important thing for the proof is how to obtain the a priori energy estimates.

2013 N 11 29 ijj 15:30  17:30
sw w 3 251
u
iRwwj
u
Nonlinear Klein-Gordon equation in de Sitter spacetime and its related topics
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The Cauchy problem for nonlinear Klein-Gordon equations is considered in de Sitter spacetime. The nonlinear terms are power type or exponential type. The local and global solutions are shown in the energy class.

2014 N 1 10 ijj 15:30  17:30
sw w 3 251
u
l iwȊwȁj
uEE
An improved level set method based on comparison with a signed distance function
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̈قȂ񑊂uĂȖʂ͊EʂƌĂ΂CԂƋɊEʂǂ̂悤ɓ𒲂ׂ邱Ƃ͊{IȖłD ʖ@́Ĉ悤ȊEʉ^͂@̈ŁCeɂȖʂ⏕֐̃[ʂƂĕ\C̕⏕֐ɑ΂ΔƂŋȖʂ̓߂D Ԃoɂĉ̌XȂ邱ƂĈƂvZ@ł͓ʂoƂƂȂD Ŗ{uł́CKɏC邱ƂŁC[ʕt߂ŌXȂȂ邱ƂCt֐Ƃ̔rʂĎD

2014 N 1 31 ijj 17:00  19:00
sw w 3 251
u
ikwȊwȁj
u
Stationary isothermic surfaces in Euclidean 3-space
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3[Nbhԓ̕sςȓʂɂāC R. Magnanini iFirenzej D. Peralta-Salas iMadridjƂ̋œꂽŋ߂̌ʂЉD Ȗ sςȓʂłƂ͔Cӂ̎ ʂɂȂĂ邱ƂD 3[Nbhԓ̗̈ lD ̋E͘AŔLEłC ̋E ̊ŐEvƂD ̕W̓֐lƂM Cauchy ̉ ̓ɕsςȓ ƂC ̋E͒ʂ~ʂɌ邱Ƃ킩D ̋ELEȂƂ͋ʂɌ邱ƂɒmĂD

2014 N 2 7 ijj 15:30  17:30
sw w 3 251
u
O j iF{wRȊwȁj
u
A monotonicity like estimate and regularity for p-harmonic map heat flows
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2014 N 2 14 ijj 15:30 ` 16:30
sw w 3 251
u
Baoxiang Wang iPeking Universityj
u
Analyticity for the Navier-Stokes equations
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