Publications of Kazumasa Fujiwara
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Research Papers
  1. K. Fujiwara, Remark on the Chain rule of fractional derivative in the Sobolev framework, to appear in Math. Inequal. Appl., arXiv: 2104.05092.
  2. K. Fujiwara, Lifespan estimates of 1D non-gauge invariant semilinear semirelativistic equations,
    Applied Mathematics Letters, 124(2022), 107619, doi: 10.1016/j.aml.2021.107619.
  3. K. Fujiwara, M. Ikeda, and Y. Wakasugi, The Cauchy problem of the semilinear second order evolution equation with fractional Laplacian and damping,
    Nonlinear Differ. Equ. Appl., 28(2021), Article Number:63, doi: 10.1007/s00030-021-00723-6, [bib:FuIkWa_2003_09239].
  4. K. Fujiwara and V. Georgiev, On global existence of $L^2$ solutions for 1D periodic NLS with quadratic nonlinearity,
    J. Math. Phys., 62(2021), 091504, doi:10.1063/5.0033101, [bib:FuGe_2009_04280].
  5. M. D'Abbicco and K. Fujiwara, A test function method for evolution equations with fractional powers of the Laplace operator,
    Nonlinear Analysis, 202(2021), 112114, doi: 10.1016/j.na.2020.112114, [Mathscinet:MR4145650].
  6. K. Fujiwara, V. Georgiev, and T. Ozawa, Self-similar solutions to the derivative nonlinear Schrodinger equation,
    J. Differential Equations, 268(2020), 7940--7961, doi: 10.1016/j.jde.2019.11.089 [Mathscinet:MR4079021].
  7. K. Fujiwara, V. Georgiev, and T. Ozawa, On global well-posedness for nonlinear semirelativistic equations in some scaling subcritical and critical cases,
    J. Math. Pures Appl., 136(2020), 239--256, doi: 10.1016/j.matpur.2019.10.003 [Mathscinet:MR4076963].
  8. K. Fujiwara, M. Ikeda, and Y. Wakasugi, Revisit on the blow-up rate of solutions for a weakly coupled system of semilinear heat equations in the subcritical case,
    Tokyo J. Math., 43 (2020), 163–-180, doi: 10.3836/tjm/1502179300, [Mathscinet:MR4121792].
  9. L. Forcella, K. Fujiwara, V. Georgiev, and T. Ozawa, Local well-posedness and blow-up for the half Ginzburg-Landau-Kuramoto equation with rough coefficients and potential,
    Discrete Contin. Dyn. Syst., 39(2019), 2661--2678, doi: 10.3934/dcds.2019111, [Mathscinet:MR3927528].
  10. K. Fujiwara, Remark on the global non-existence of semirelativistic equations with non-gauge invariant power type nonlinearity with mass,
    Pliska Stud. Math., 30(2019), 71--84. arXiv:1809.10202, [Mathscinet:MR3898132].
  11. K. Fujiwara, A note for the global non-existence of semirelativistic equations with non-gauge invariant power type nonlinearity,
    Math Meth Appl Sci., 41 (2018), 4955--4966, doi:10.1002/mma.4944, [Mathscinet:MR3843572].
  12. K. Fujiwara, M. Ikeda, and Y. Wakasugi, Estimates of lifespan and blow-up rates for the wave equation with a time-dependent damping and a power-type nonlinearity,
    Funkcial. Ekvac., 62(2019), 157--189, doi:https://doi.org/10.1619/fesi.62.157, [Mathscinet:MR3970099].
  13. K. Fujiwara, V. Georgiev, and T. Ozawa, Blow-up for self-interacting fractional Ginzburg-Landau equation,
    Dyn. Partial Differ. Equ., 15 (2018), 175 -- 182. doi:10.4310/DPDE.2018.v15.n3.a1, [Mathscinet:3809638].
  14. K. Fujiwara, V. Georgiev, and T. Ozawa, Higher order fractional Leibniz rule,
    J. Fourier Anal. Appl. 24 (2018), 650--665, doi:10.1007/s00041-017-9541-y, [Mathscinet:MR3802288].
  15. K. Fujiwara and T. Ozawa, On the lifespan of strong solutions to the periodic derivative nonlinear Schr\"odinger equation,
    Evol. Equ. Control Theory, 7(2017), 275--280, doi:10.3934/eect.2018013, [Mathscinet:MR3809638].
  16. K. Fujiwara, M. Ikeda and Y. Wakasugi, Blow-up of solutions for weakly coupled systems of complex Ginzburg-Landau equations,
    Electron. J. Differential Equations, 2017 (2017), No. 196, 1-18, [Link], [Mathscinet:MR3690223].
  17. K. Fujiwara and T. Ozawa, Lifespan of strong solutions to the periodic nonlinear Schr\"odinger equation without gauge invariance,
    J. Evol. Equ., 17 (2017), 1023--1030, doi:10.1007/s00028-016-0364-0, [Mathscinet:MR3707307].
  18. K. Fujiwara and T. Ozawa, Finite time blowup of solutions to the nonlinear Schr\"odinger equation without gauge invariance,
    J. Math. Phys., 57(2016), 082103, doi:10.1063/1.4960725, [bib:MR3535686].
  19. K. Fujiwara and T. Ozawa, Weighted $L^p$-boundedness of convolution type integral operators associated with bilinear estimates in the Sobolev spaces,
    J. Math. Soc. Japan, 68(2016), 169--191, doi:10.2969/jmsj/06810169, [Mathscinet:MR3454558].
  20. K. Fujiwara, Remark on local solvability of the Cauchy problem for semirelativistic equations,
    J. Math. Anal. Appl., 432 (2015), 744--748, doi:10.1016/j.jmaa.2015.07.009, [Mathscinet:MR3378389].
  21. K. Fujiwara and T. Ozawa, Remarks on global solutions to the Cauchy problem for semirelativistic equations with power type nonlinearity,
    Int. J. Math. Anal., 9(2015), 2599--2610, doi:10.12988/ijma.2015.58211, [Mathscinet:MR3378389].
  22. K. Fujiwara, S. Machihara, and T. Ozawa, On a system of semirelativistic equations in the energy space,
    Comm. Pure Appl. Anal., 14 (2015), 1343--1355, doi:10.3934/cpaa.2015.14.1343, [Mathscinet:MR3359524].
  23. K. Fujiwara, S. Machihara, and T. Ozawa, Well-posedness for the Cauchy problem for a system of semirelativistic equations,
    Comm. Math. Phys., 338(2015), 367--391, doi:10.1007/s00220-015-2347-3. [Mathscinet:MR3345380]
  24. K. Fujiwara and T. Ozawa, Identities for the difference between the arithmetic and geometric means,
    Int. J. Math. Anal., 8 (2014), 1525--1542, doi:10.12988/ijma.2014.46170, [bib:FuOz14Id].
  25. K. Fujiwara and T. Ozawa, Stability of the Young and Holder inequalities,
    J. Inequal. Appl., 2014:162, doi:10.1186/1029-242X-2014-162, [Mathscinet:MR3346834].
  26. K. Fujiwara and T. Ozawa, Exact remainder formula for the Young inequality and applications,
    Int. J. Math. Anal., 7 (2013), 2723--2735, doi:10.12988/ijma.2013.39230, [Mathscinet:MR3152987].
Proceedings (with peer review)
  1. L. Forcella, K. Fujiwara, V. Georgiev, and T. Ozawa, Blow-up or global existence for the fractional Ginzburg-Landau equation in multi-dimensional case,
    New Tools for Nonlinear PDEs and Applications, Birkh\"auser Basel, 179--202 (2019). [Mathscinet:MR4011367]
  2. K. Fujiwara and H. Miyazaki, The derivation of conservation laws for nonlinear Schr\"odinger equations with power type nonlinearities,
    RIMS Kokyuroku Bessatsu, B63, 13--21(2017), [Mathscinet:MR3751978].
  3. K. Fujiwara and T. Ozawa, Remarks on bilinear estimates in the Sobolev spaces,
    RIMS Kokyuroku Bessatsu, B56, 1--9 (2016), [Mathscinet:MR3617712].
  4. K. Fujiwara, S. Machihara, and T. Ozawa, Remark on a semirelativistic equation in the energy space,
    Discrete Contin. Dyn. Syst. 2015, Dynamical systems, differential equations and applications. 10th AIMS Conference. Suppl., 473--478 (2015),
  5. doi:10.3934/proc.2015.0473, [Mathscinet:MR3462480].
Submitted Papers
  1. K. Fujiwara, Note on the lifespan estimate of solutions for non-gauge invariant semilinear massless semirelativistic equations with some scaling critical nonlinearity, [arXiv:2109.00030].
Theses