## CONCEPTPapers

■Preprints:
1. Yoshiyuki Kagei and Hiroshi Takeda, Smoothing effect and asymptotic behavior of solutions to nonlinear elastic wave equations with viscoelastic terms in the framework of Lp-Sobolev spaces, preprint, 2021, arXiv:2109.04618

■Papers:
1. Yoshiyuki Kagei and Hiroshi Takeda, Smoothing effect and large time behavior of solutions to nonlinear elastic wave equations with viscoelastic term, accepted in Nonlinear Analysis (arXiv:2109.04628)
2. Yoshiyuki Kagei, On the mathematical analysis of the artificial compressibility method. Partial Differ. Equ. Appl. 2 (2021), no. 5, 65. https://doi.org/10.1007/s42985-021-00118-3
3. Chun-Hsiung Hsia, Yoshiyuki Kagei, Takaaki Nishida and Yuka Teramoto, Singular limit in Hopf bifurcation for doubly diffusive convection equations II: bifurcation and stability, J. Math. Fluid Mech. 23 (2021), no. 3, Paper No. 59. https://doi.org/10.1007/s00021-021-00583-1 (arXiv:2103.02779)
4. Chun-Hsiung Hsia, Yoshiyuki Kagei, Takaaki Nishida and Yuka Teramoto, Singular limit in Hopf bifurcation for doubly diffusive convection equations I: linearized analysis at criticality, J. Math. Fluid Mech. 23 (2021), no. 3, Paper No. 60. https://doi.org/10.1007/s00021-021-00582-2 (arXiv:2103.02778)
5. Mohamad Nor Azlan, Shota Enomoto and Yoshiyuki Kagei, On the spectral properties for the linearized problem around space-time periodic states of the compressible Navier-Stokes equations, Mathematics 2021, 9(7), 696.

https://doi.org/10.3390/math9070696

6. Yoshiyuki Kagei and Yuka Teramoto, On the spectrum of the linearized operator around compressible Couette flows between two concentric cylinders, J. Math. Fluid Mech., {\bf 22} (2020), no. 2, Article no. 21, 23 pages. https://doi.org/10.1007/s00021-020-0485-7
7. Abulizi Aihaiti and Yoshiyuki Kagei, Asymptotic behavior of solutions of the compressible Navier-Stokes equations in a cylinder under the slip boundary condition, Math. Methods Appl. Sci., {\bf 42} (2019), no. 10, pp. 3428–-3464.
8. Yoshiyuki Kagei and Takaaki Nishida, Traveling waves bifurcating from plane Poiseuille flow of the compressible Navier-Stokes equation, Arch. Rational Mech. Anal., {\bf 231} (2019), no. 1, pp. 1--44.
9. Yoshiyuki Kagei, Takaaki Nishida and Yuka Teramoto, On the spectrum for the artificial compressible system, J. Differential Equations, {\bf 264} (2018), no. 2, pp. 897--928.
10. Shota Enomoto and Yoshiyuki Kagei, Asymptotic behavior of the linearized semigroup at space-periodic stationary solution of the compressible Navier-Stokes equation, J. Math. Fluid Mech., {\bf 19} (2017), no. 4, pp. 739--772.
11. Yoshiyuki Kagei and Takaaki Nishida, On Chorin's method for stationary solutions of the Oberbeck-Boussinesq equation, J. Math. Fluid Mech., {\bf 19} (2017), no. 2, pp. 345--365. DOI: 10.1007/s00021-016-0284-3
12. Abulizi Aihaiti, Shota Enomoto, Yoshiyuki Kagei, Large time behavior of solutions to the compressible Navier-Stokes equations in an infinite layer under slip boundary condition, Math. Models Meth. Appl. Sci., {\bf 26} (2016), no.14, pp.2617--2649. DOI: http://dx.doi.org/10.1142/S0218202516500615
13. Yoshiyuki Kagei and Masatoshi Okita, Asymptotic profiles for the compressible Navier-Stokes equations on the whole space, J. Math. Anal. Appl., {\bf 445} (2017), no. 1, pp. 297--317. http://doi.org/10.1016/j.jmaa.2016.07.024
14. Yoshiyuki Kagei and Michael Ruzicka, The Oberbeck-Boussinesq approximation as a constitutive limit, Continuum Mechanics and Thermodynamics {\bf 28} (2016), no. 5, pp. 1411--1419. DOI 10.1007/s00161-015-0483-9
15. Yoshiyuki Kagei and Ryouta Oomachi, Stability of time periodic solution of the Navier-Stokes equation on the half-space under oscillatory moving boundary condition, J. Differential Equations {\bf 261} (2016), pp. 3366--3413.
16. Reika Aoyama and Yoshiyuki Kagei, Spectral properties of the semigroup for the linearized compressible Navier-Stokes equation around a parallel flow in a cylindrical domain, Advances in Differential Equations {\bf 21} (2016), no. 3-4, pp. 265--300.
17. Reika Aoyama and Yoshiyuki Kagei, Large time behavior of solutions to the compressible Navier-Stokes equations around a parallel flow in a cylindrical domain, Nonlinear Analysis Series A: Theory, Methods and Applications {\bf 127} (2015), pp. 362--396. doi:10.1016/j.na.2015.07.009
18. Yoshiyuki Kagei and Naoki Makio, Spectral properties of the linearized semigroup of the compressible Navier-Stokes equation on a periodic layer,
Publ. Res. Inst. Math. Sci., {\bf 51}, no. 2 (2015), pp. 337--372.
19. Yoshiyuki Kagei and Takaaki Nishida, Instability of plane Poiseuille flow in viscous compressible gas, J. Math. Fluid Mech., vol. 17 (2015),no.1, pp. 129--143. DOI: 10.1007/s00021-014-0191-4
20. Yoshiyuki Kagei and Kazuyuki Tsuda, Existence and stability of time periodic solution to the compressible Navier-Stokes equation for time periodic external force with symmetry, J. Differential Equations, vol. 258 (2015), pp. 399--444.
21. Jan Brezina and Yoshiyuki Kagei, Spectral properties of the linearized compressible Navier-Stokes equation around time-periodic parallel flow, J. Differential Equations, vol. 255 (2013), no. 6, pp. 1132--1195.
22. Yoshiyuki Kagei and Yasunori Maekawa,On asymptotic behaviors of solutions to parabolic systems modelling chemotaxis, J. Differential Equations, vol. 253 (2012), no.11, pp. 2951--2992.
23. Yoshiyuki Kagei, Asymptotic behavior of solutions to the compressible Navier-Stokes equation around a parallel flow, Arch. Rational Mech. Anal. vol. 205 (2012), no. 2, pp. 585--650.
24. Jan Brezina and Yoshiyuki Kagei, Decay properties of solutions to the linearized compressible Navier-Stokes equation around time-periodic parallel flow, Math. Models Meth. Appl. Sci., vol. 22 (2012), 1250007 (53 pages).
25. Yoshiyuki Kagei, Global existence of solutions to the compressible Navier-Stokes equation around parallel flows, J. Differential Equations, vol. 251 (2011), no. 11, pp. 3248--3295.
26. Yoshiyuki Kagei and Yasunori Maekawa, Asymptotic behaviors of solutions to evolution equations in the presence of translation and scaling invariance, J. Functional Analysis, vol. 260 (2011), no. 10, pp. 3036--3096.
27. Yoshiyuki Kagei, Asymptotic behavior of solutions of the compressible Navier-Stokes equation around the plane Couette flow, J. Math. Fluid Mech., vol. 13 (2011), no. 1, pp. 1--31.
28. Yoshiyuki Kagei, Yu Nagafuchi and Takeshi Sudou, Decay estimates on solutions of the linearized compressible Navier-Stokes equation around a Poiseuille type flow, Journal of Math-for-Industory, vol. 2 (2010A), pp. 39--56. Correction to "Decay estimates on solutions of the linearized compressible Navier-Stokes equation around a Poiseuille type flow" in J. Math-for-Ind., vol. 2 (2010A), pp. 39--56, J. Math-for-Ind., vol. 2 (2010B), pp. 235.
29. Yuya Ishihara and Yoshiyuki Kagei, Large time behavior of the semigroup on $L^p$ spaces associated with the linearized compressible Navier-Stokes equation in a cylindrical domain, J. Differential Equations, vol. 248 (2010), no. 2, pp. 252--286.
30. Yoshiyuki Kagei and Takumi Nukumizu, Asymptotic behavior of solutions to the compressible Navier-Stokes equation in a cylindrical domain, Osaka J. Math., vol. 45 (2008), no. 4, pp. 987--1026.
31. Yoshiyuki Kagei, Large time behavior of solutions to the compressible Navier-Stokes equation in an infinite layer, Hiroshima Math. J., vol. 38 (2008), no. 1, pp. 95 -- 124.
32. Yoshiyuki Kagei, Asymptotic behavior of the semigroup associated with the linearized compressible Navier-Stokes equation in an infinite layer, Publ. Res. Inst. Math. Sci., vol. 43 (2007), no. 3, pp. 763--794.
33. Resolvent estimates for the linearized compressible Navier-Stokes equation in an infinite layer, Yoshiyuki Kagei, Funkcial. Ekvac., vol.50 (2007),no. 2, pp. 287--337.
34. Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space, Yoshiyuki Kagei and Shuichi Kawashima, Commun. Math. Phys., vol.266 (2006), no. 2, pp.401 -- 430.
35. Yoshiyuki Kagei and Shuichi Kawashima, Local solvability of initial boundary value problem for a quasilinear hyperbolic-parabolic system, Journal of Hyperbolic Differential Equations, vol.3 (2006), no. 2, pp.195 -- 232.
36. Yoshiyuki Kagei and Takayuki Kobayashi, Asymptotic behavior of solutions to the compressible Navier-Stokes equations on the half space, Arch. Ration. Mech. Anal. vol. 177 (2005), no. 2, pp. 231 -- 330.
37. A limit problem in natural convection, Yoshiyuki Kagei, Michael Ruzicka and Gudrun Thaeter, Nonlinear Differential Equations Appl., vol. 13 (2006), no. 4, pp. 447--467.
38. On large-time behavior of solutions to the compressible Navier-Stokes equations in the half space in $R^3$, Yoshiyuki Kagei, Takayuki Kobayashi, Arch. Ration. Mech. Anal. , vol. 165 (2002), no. 2, pp.89--159.
39. Yoshiyuki Kagei, Invariant manifolds and long-time asymptotics for the Vlasov-Poisson-Fokker-Planck equation, SIAM J. Math. Anal., vol. 33 (2001), no. 2, pp.489--507.
40. Yoshiyuki Kagei, Michael Ruzicka, Gudrun, Natural convection with dissipative heating, Commun. Math. Phys. , vol. 214 (2000), no. 2, pp.287--313.
41. Yoshiyuki Kagei and Wolf von Wahl, Asymptotic stability of steady flows in infinite layers of viscous incompressible fluids in critical cases of stability, Indiana Univ. Math. J., vol. 48 (1999), no. 3, pp.1083--1110.
42. Yoshiyuki Kagei and Wolf von Wahl, The Eckhaus criterion for convection roll solutions of the Oberbeck-Boussinesq equations, Internat. J. Non-Linear Mech. , vol. 32 (1997), no. 3, pp.563--620.
43. Yoshiyuki Kagei and Wolf von Wahl, Asymptotic stability of higher order norms in terms of asymptotic energy stability for viscous incompressible fluid flows heated from below, Japan J. Indust. Appl. Math. , vol. 13 (1996), no. 1, pp.33 --49.
44. Yoshiyuki Kagei, Attractors for two-dimensional equations of thermal convection in the presence of the dissipation function, Hiroshima Math. J., vol. 25 (1995), no. 2, pp.251--311.
45. Yoshiyuki Kagei and Wolf von Wahl, Stability of higher norms in terms of energy-stability for the Boussinesq equations: remarks on the asymptotic behaviour of convection-roll-type solutions, Differential Integral Equations, vol.7 (1994), pp.921--948.
46. Yoshiyuki Kagei, On weak solutions of nonstationary Boussinesq equations, Differential Integral Equations, vol.6 (1993), pp.587--611.
47. Yoshiyuki Kagei and Maria Skowron, Nonstationary flows of nonsymmetric fluids with thermal convection, Hiroshima Math. J, vol. 23 (1993), no. 2, pp.343--363.
48. Zhi Min Chen, Yoshiyuki Kagei and Tetsuro Miyakawa, Remarks on stability of purely conductive steady states to the exterior Boussinesq problem, Adv. Math. Sci. Appl., vol. 1 (1992), no. 2, pp. 411--430.

■Proceedings:
1. Yoshiyuki Kagei, On Stability and Bifurcation in Parallel Flows of Compressible Navier-Stokes Equations, Nonlinear Partial Differential Equations for Future Applications, Sendai, Japan, July 10–28 and October 2–6, 2017, editors: Shigeaki Koike, Hideo Kozono, Takayoshi Ogawa, Shigeru Sakaguchi, Springer Proceedings in Mathematics & Statistics, vol. 346, pp. 71--93, 2021. https://doi.org/10.1007/978-981-33-4822-6
2. Yoshiyuki Kagei, On the Chorin method for thermal convection equations for viscous incompressible fluids, Regularity, singularity and long time behavior for partial differential equations with conservation law, RIMS Kôkyûroku Bessatsu B80, pp. 95--112, eds. Keiichi Kato, Mishio Kawashita, Masashi Misawa, Takayoshi Ogawa, April, 2020.

3. Yoshiyuki Kagei, On stationary bifurcation problem for the compressible Navier-Stokes equations, Hyperbolic Problems: Theory, Numerics, Applications, pp. 192--202, Alberto Bressan, Marta Lewicka, Dehua Wang, Yuxi Zheng (Eds.), American Institute of Mathematical Sciences, 2020, published online:

https://www.aimsciences.org/book/AM/volume/Volume%2010

4. Yoshiyuki Kagei, On asymptotic behavior of solutions of the compressible Navier-Stokes equation around a parallel flow, Proceedings of the conference "Hyperbolic Problems: Theory, Numerics and Applications" (HYP2010), Series in Contemporary Applied Mathematics CAM 17 (Editors: Tatsien Li and Song Jiang), vol. 1, pp. 44--59, July, 2012, Higher Education Press (Beijing).
5. Yoshiyuki Kagei, On large time behavior of solutions to the compressible Navier-Stokes equation in an infinite layer, Yoshiyuki Kagei, to appear in the Proceedings of "Mathematical Analysis on the Navier-Stokes equations and Related Topics, Past and Future, --In memory of Professor Tetsuro Miyakawa", Gakuto International Series Mathematical Sciences and Applications., vol. 35 (2011), pp. 71--90.
6. Yoshiyuki Kagei, On two-dimensional equations of thermal convection in the presence of the dissipation function, Theory of the Navier-Stokes equations, Ser. Adv. Math. Appl. Sci., 47, pp.72--85, 1998.