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Affiliation Department |
Department of Computer Science
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Associate Professor |
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External Link |
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CHIKAMI Noboru
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External Career
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Tohoku University Graduate School of Science Assistant Professor
2016.06 - 2018.03
Country：Japan
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Osaka University Graduate School of Engineering Science Special researcher of the Japan Society for the Promotion of Science
2018.04 - 2019.12
Country：Japan
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Osaka University Graduate School of Engineering Science Lecturer
2019.04 - 2019.12
Country：Japan
Papers
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Optimal well-posedness and forward self-similar solution for the Hardy-Hénon parabolic equation in critical weighted Lebesgue spaces Reviewed
Chikami, Noboru; Ikeda, Masahiro; Taniguchi, Koichi
Nonlinear Anal. 222 2022.09
Authorship：Corresponding author Publishing type：Research paper (scientific journal)
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Well-posedness and global dynamics for the critical Hardy-Sobolev parabolic equation Reviewed International journal
Noboru Chikami, Masahiro Ikeda, Koichi Taniguchi
Nonlinearity 34 ( 11 ) 2021.10
Language：English Publishing type：Research paper (scientific journal) Publisher：IOP Publishing Ltd & London Mathematical Society
Other Link： https://iopscience.iop.org/article/10.1088/1361-6544/ac2c90
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Composition estimates and well-posedness for Hardy–Hénon parabolic equations in Besov spaces Reviewed
Noboru Chikami
Journal of Elliptic and Parabolic Equations 2019.12
Publishing type：Research paper (scientific journal) Publisher：Springer Science and Business Media {LLC}
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Global Well-Posedness and Time-Decay Estimates of the Compressible Navier–Stokes–Korteweg System in Critical Besov Spaces Reviewed
Noboru Chikami, Takayuki Kobayashi
Journal of Mathematical Fluid Mechanics 21 ( 2 ) 2019.06
Publishing type：Research paper (scientific journal) Publisher：Springer Science and Business Media {LLC}
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On Gagliardo-Nirenberg type inequalities in Fourier-Herz spaces Reviewed
Chikami Noboru
JOURNAL OF FUNCTIONAL ANALYSIS 275 ( 5 ) 1138 - 1172 2018.09
Language：English Publishing type：Research paper (scientific journal)
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On the global existence and time decay estimates in critical spaces for the Navier-Stokes-Poisson system Reviewed International coauthorship
Noboru Chikami, Raphael Danchin
MATHEMATISCHE NACHRICHTEN 290 ( 13 ) 1939 - 1970 2017.09
Language：English Publishing type：Research paper (scientific journal) Publisher：WILEY-V C H VERLAG GMBH
We are concerned with the study of the Cauchy problem for the Navier-Stokes-Poisson system in the critical regularity framework. In the case of a repulsive potential, we first establish the unique global solvability in any dimension n >= 2 for small perturbations of a linearly stable constant state. Next, under a suitable additional condition involving only the low frequencies of the data and in the L-2-critical framework (for simplicity), we exhibit optimal decay estimates for the constructed global solutions, which are similar to those of the barotropic compressible Navier-Stokes system. Our results rely on new a priori estimates for the linearized Navier-Stokes-Poisson system about a stable constant equilibrium, and on a refined time-weighted energy functional. (C) 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Other Link： http://orcid.org/0000-0002-3107-2088
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Well-posedness of the compressible Navier-Stokes-Poisson system in the critical Besov spaces Reviewed
Noboru Chikami, Takayoshi Ogawa
JOURNAL OF EVOLUTION EQUATIONS 17 ( 2 ) 717 - 747 2017.06
Language：English Publishing type：Research paper (scientific journal) Publisher：SPRINGER BASEL AG
We consider the Cauchy problem of the compressible Navier-Stokes system coupled with a Poisson equation. We give the optimal well-posedness in terms of scaling in the Besov framework. The results include the case of two dimensions, which is not treated in previous results.
DOI： 10.1007/s00028-016-0334-6
Other Link： http://orcid.org/0000-0002-3107-2088
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WELL-POSEDNESS OF THE COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM IN BESOV SPACES (Mathematical Analysis in Fluid and Gas Dynamics)
Chikami Noboru, Ogawa Takayoshi
RIMS Kokyuroku ( 1985 ) 144 - 158 2016.04
Language：English Publishing type：Research paper (scientific journal) Publisher：Kyoto University
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On the well-posedness of the full compressible Navier-Stokes system in critical Besov spaces Reviewed International coauthorship
Noboru Chikami, Raphael Danchin
JOURNAL OF DIFFERENTIAL EQUATIONS 258 ( 10 ) 3435 - 3467 2015.05
Language：English Publishing type：Research paper (scientific journal) Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE
We are concerned with the Cauchy problem of the full compressible Navier Stokes equations satisfied by viscous and heat conducting fluids in R-n. We focus on the so-called critical Besov regularity framework. In this setting, it is natural to consider initial densities rho(0), velocity fields u(0) and temperatures theta(0) with a(0) := rho(0) - 1 is an element of (B) over dot(p,1)(n/p), u(0) is an element of (B) overp dot(p,1)(n/p-1) and theta(0) (B)over dot(p,1)(n/p-2). After recasting the whole system in Lagrangian coordinates, and working with the total energy along the flow rather than with the temperature, we discover that the system may be solved by means of Banach fixed point theorem in a critical functional framework whenever the space dimension is n >= 2, and 1 < p < 2n. Back to Eulerian coordinates, this allows to improve the range of p's for which the system is locally well-posed, compared to [7]. (C) 2015 Elsevier Inc. All rights reserved.
DOI： 10.1016/j.jde.2015.01.012
Other Link： http://orcid.org/0000-0002-3107-2088
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THE BLOW-UP CRITERION FOR THE COMPRESSIBLE NAVIER-STOKES SYSTEM WITH A YUKAWA-POTENTIAL IN THE CRITICAL BESOV SPACE Reviewed
Noboru Chikami
DIFFERENTIAL AND INTEGRAL EQUATIONS 27 ( 9-10 ) 801 - 820 2014.09
Language：English Publishing type：Research paper (scientific journal) Publisher：KHAYYAM PUBL CO INC
We give a refined blow-up criterion for the solution for the compressible Navier-Stokes system with a Yukawa-potential in the critical Besov space [13]. The result may be considered as a compressible counterpart of the results for. the incompressible Navier-Stokes system.
Other Link： http://orcid.org/0000-0002-3107-2088
Presentations
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Solvability of the stationary compressible Navier-Stokes-Korteweg system Invited International conference
Noboru Chikami
Workshop on Evolution Equations 2022.10 L. Aloui, J. Hedhly, S. Tayachi
Event date： 2022.10
Language：English Presentation type：Oral presentation (invited, special)
Venue：University of Tunis El Manar Country：Tunisia
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Unconditional uniqueness and non-uniqueness for Hardy-He ́non parabolic equations Invited International coauthorship International conference
Noboru Chikami
Notiziario dei seminari di carattere matematico 2022.09 Department of Mathematics Sapienza University of Rome
Event date： 2022.09
Language：English Presentation type：Oral presentation (general)
Venue：Rome Country：Italy
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Optimal well-posedness of Hardy–H ́enon parabolic equation
千頭昇
日本数学会2021年度秋季分科会 千葉大学
Event date： 2021.09
Language：English Presentation type：Oral presentation (general)
Venue：千葉大学
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Optimal well-posedness and forward self-similar solution for the Hardy-He ́non parabolic equation International conference
Noboru Chikami
13th International ISAAC Congress ISAAC, Ghent University
Event date： 2021.08
Language：English Presentation type：Oral presentation (general)
Venue：Ghent, Belgium
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Hardy-H'enon parabolic equation in weighted Lebesgue space Invited
千頭昇
名古屋微分方程式セミナー 杉本充，菱田俊明，加藤淳，寺澤祐高
Event date： 2021.04
Language：Japanese Presentation type：Oral presentation (general)
Venue：名古屋大学
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Hardy-H¥'enon型半線型熱方程式の解の挙動 International conference
千頭昇，谷口晃一，池田正弘
日本数学会2020年度秋季分科会 日本数学会
Event date： 2020.09
Language：Japanese Presentation type：Oral presentation (general)
Venue：熊本大学（オンライン開催）
Scientific Research Funds Acquisition Results
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燃焼と流体の大域ダイナミクス解析
2021.04
科学研究費補助金 若手研究
千頭昇
本研究の目的は，流体力学の基礎方程式である Navier-Stokes 系や，燃焼や化学反応系，人口密 度，天体構造等の時間発展を記述する半線形熱方程式の適切性や解の安定性・大域ダイナミクスを 解析することである.物理数学に現れる多くの非線形偏微分方程式は，非線形項の形によっては 変分構造を持ち，何らかの形で解を制御する固有の物理量が現れる.このような物理量が時間に 関して単調性を持つ時，これによって時間大域的な解のダイナミクスや安定性，特異性形成，ま た，対応する定常問題のソリトン的な特殊解が果たす解の漸近挙動への影響等が解析できる.本 研究では，必要な解析技術の整備を行い，主に解の臨界正則性に着眼し，流体や燃焼の物理方程 式の適切性・安定性解析と，解の挙動の初期値による詳細な分類を目指す.
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調和解析による圧縮性粘性流体の臨界適切性理論の構築
2018.04 - 2019.12
科学研究費補助金 特別研究員奨励費
千頭昇
様々な物理的設定の下で, 圧縮性粘性流体を記述する基礎方程式系と, 関連する初期値問題の「臨界適切性」について, 関数解析学的・調和解析学的な手法を用いた研究を行う.
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圧縮性粘性流体と関連する諸問題の安定性解析
2017.04
科学研究費補助金 若手研究(B)
千頭昇
本研究の目的は気体力学の基礎方程式である圧縮性 Navier-Stokes 系の臨界適切性を示し, 解の安定性, 及び時間無限大での漸近挙動を解析することである. 圧縮性 Navier-Stokes 系は, 圧力の変化に応じて密度が変位する圧縮性流れを数学的に定式化したモデルであり, 状態方程式の選び方によって様々な気体状態を表す. 偏微分方程式論の観点からは, 多くの圧縮性流れは非線形の双曲型放物型混合系で表され, 斉次非圧縮性粘性流体と異なり, 密度遷移に由来する分散性と, 粘性に由来するエネルギー消散の両方が流れに影響を及ぼす. 本研究では主に解の臨界正則性に着眼し圧縮性流れの解析を行い, 初期摂動が高速振動する流れを含む場合の気体力学の安定性理論の構築を目標とする.
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圧縮性 Navier-Stokes-Poisson 系の解の存在と挙動について
2013.04 - 2015.03
科学研究費補助金 特別研究員奨励費
千頭昇
流体力学の基礎方程式の一つである圧縮性 Navier-Stokes 系に対する適切性の考察．