# MBZ~i[

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## 30Nx

4 2018N 12 17() 16:30 - 18:00

ut: ߌTV (cw)

: Well-posedness and ill-posedness of the stationary Navier-Stokes equations in the scaling invariant Besov space

Tv: 񈳏kNavier-Stokes̃XP[sςBesovԂɂKؐ i^ꂽO͂ɘAIɈˑ̈ӑݐjєKؐɂčl@. {uł͓ɔKؐɏœ_𓖂, O͂̋Ԃ̈ʑ߂ ̘Aˑꍇ邱Ƃؖ. {Cunanan-Okabe-Tsutsui (2017) Kaneko-Kozono-Shimizu (2017) ɂKؐɊւsʂ, BesovԂ̘gg݂ŊTˍœKł邱Ƃ̂ł.

## ȑO̍u

3 2017N 2 20() 16:30 - 18:00

ut: v (kw)

: Asymptotic expansions of solutions of fractional diffusion equations

Tv: We obtain the precise description of the asymptotic behavior of the solution $u$ of $\partial_t u+(-\Delta)^{\frac{\theta}{2}}u=0$ in ${\bf R}^N\times(0,\infty)$, $u(x,0)=\varphi(x)$ in ${\bf R}^N$, where $0<\theta<2$ and $\varphi\in L_K:=L^1({\bf R}^N,\,(1+|x|)^K\,dx)$ with $K\ge 0$. Furthermore, we develop the arguments in Ishige-Kawakami (2012) and Ishige-Kawakami-Kobayashi (2014) and establish a method to obtain the asymptotic expansions of the solutions to a nonlinear fractional diffusion equation $\partial_t u+(-\Delta)^{\frac{\theta}{2}}u=|u|^{p-1}u$ in ${\bf R}^N\times(0,\infty)$, where $0<\theta<2$ and $p>1+\theta/N$. Joint work with Kazuhiro Ishige and Tatsuki Kawakami.

2 2016N 12 9 () 16:30-18:00

ut: FM (sw)

: The Wolff potential estimate for solutions to elliptic equations with signed data

Tv: $p$-Da֐ɑ΂ Wolff |eVɂe_]ɂčl. ̕], $p$-a֐ Wiener ̔̕Kv̂ Kilpel{\"a}inen-Mal{\'y} (1994) ɂēꂽ. Trudinger-Wang (2002) ͂̕] Poisson ό𗘗pVؖ^. Duzaar-Mingione (2010) ͌z]̐V@p, $p \geq 2$ ̏ꍇɕtO͂ɑ΂ɑ΂Ăގ̊e_]^. {uł, Poisson ό Kilpel{\"a}inen-Mal{\'y} ̎@gݍ킹邱Ƃ, 2̕] $1 < p < 2$ tO͂̏ꍇ܂߂Vؖ^.

1 2016N 11 11 () 16:30-18:00

ut: Chris Jeavons (cw)

: On sharp linear and bilinear Strichartz inequalities

Tv: In recent years the problem of determining best constants and the shape of maximisers for well-known functional inequalities has attracted considerable attention, but has proved difficult in general. In my talk I will present some progress on this problem for the classical Strichartz inequalities for the wave and Klein--Gordon equations. In each case, our proof combines a bilinear estimate with techniques developed recently in the study of closely-related Fourier restriction inequalities. The bilinear estimates we prove are interesting in their own right; if time permits I will discuss some further applications of these results.
The talk will be based on a number of joint works with Neal Bez, Hiroki Saito and Tohru Ozawa

## WXg

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tsutsui(at)shinshu-u.ac.jp