Research Papers
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K. Fujiwara and V. Georgiev,
A new class of small initial data which may shift the critical power and lifespan estimates for the classical damped wave equations,
to appear in Evol. Equ. Control Theory.
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K. Fujiwara,
Note on the lifespan estimate of solutions for non-gauge invariant semilinear massless semirelativistic equations with some scaling critical nonlinearity,
to appear in Journal of Evolution Equations,
doi:10.1007/s00028-022-00865-9.
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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,
[Mathscinet: MR4307926].
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K. Fujiwara,
Remark on the Chain rule of fractional derivative in the Sobolev framework,
Math. Inequal. Appl.,
24(2021),
1113--1124,
doi: dx.doi.org/10.7153/mia-2021-24-77,
[Mathscinet: MR4364567].
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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].
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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].
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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].
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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].
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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].
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K. Fujiwara, M. Ikeda, and Y. Wakasugi,
Lifespan of solutions for a weakly coupled system of semilinear heat equations,
Tokyo J. Math.,
43 (2020),
163–-180,
doi: 10.3836/tjm/1502179300,
[Mathscinet: MR4121792].
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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].
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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].
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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].
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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].
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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: MR3809638].
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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].
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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].
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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].
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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].
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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].
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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].
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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].
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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].
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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].
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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].
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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].
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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].
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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)
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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].
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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].
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K. Fujiwara and T. Ozawa,
Remarks on bilinear estimates in the Sobolev spaces,
RIMS Kokyuroku Bessatsu, B56, 1--9 (2016),
[Mathscinet:MR3617712].
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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),
doi:10.3934/proc.2015.0473,
[Mathscinet:MR3462480].
Submitted Papers
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K. Fujiwara and V. Georgiev,
On extended lifespan for 1d damped wave equation,
arXiv:2212.13845
Theses