Towards regularity

Results

The joint research has contributed to the following works:

2013

  • Y. Giga, P. Górka, P. Rybka, Evolution of regular bent rectangles by the driven crystalline curvature flow in the plane with a non-uniform forcing term, Adv. Differential Equations 18 (2013), no. 3-4, 201—242 (link)
  • H. Jia, G. Seregin, G.; V.A. Šverák, Liouville theorem for the Stokes system in half-space. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 410 (2013), Kraevye Zadachi Matematicheskoi Fiziki i Smezhnye Voprosy Teorii Funktsii. 43, 25—35, 187; reprinted in J. Math. Sci. (N.Y.) 195 (2013), no. 1, 13—19 (link)
  • K. Abe, Y. Giga, Analyticity of the Stokes semigroup in spaces of bounded functions. Acta Math. 211 (2013), no. 1, 1—46 (link)
  • Y. Giga, N. Hamamuki, Hamilton-Jacobi equations with discontinuous source terms. Comm. Partial Differential Equations 38 (2013), no. 2, 199—243 (link)
  • M.-H. Giga, Y. Giga, A. Nakayasu, On general existence results for one-dimensional singular diffusion equations with spatially inhomogeneous driving force. Geometric partial differential equations, 145—170, CRM Series, 15, Ed. Norm., Pisa, 2013 (link)
  • M.-H. Giga, Y. Giga and N. Požár, Nenseikai riron ni yoru Kyotokui Kakusan Hoteishiki no sugaku kaiseki. Ijokakusan no Suri, RIMS Kôkyûroku (in Japanese) 1854 (2013), 57—77.
  • R. Farwig, C. Komo, Optimal initial value conditions for local strong solutions of the Navier-Stokes equations in exterior domains. Analysis (Munich) 33 (2013), no. 2, 101—119 (link)
  • M.-H. Giga, Y. Giga，Ketshoseicho mondai to Kyotokui Kakusan Hoteishiki. Ijokakusan no Suri, RIMS Kôkyûroku (in Japanese) 1854 (2013), 33—56.
  • Y. Giga, G. Pisante, On representation of boundary integrals involving the mean curvature for mean-convex domains. Geometric partial differential equations, 171—187, CRM Series, 15, Ed. Norm., Pisa, 2013 (link)
  • M.-H. Giga, Y. Giga, T. Ohtsuka, N. Umeda, On behavior of signs for the heat equation and a diffusion method for data separation. Commun. Pure Appl. Anal. 12 (2013), no. 5, 2277—2296 (link)
  • G. Seregin, T. Shilkin, The local regularity theory for the Navier-Stokes equations near the boundary. Proceedings of the St. Petersburg Mathematical Society. Vol. XV. Advances in mathematical analysis of partial differential equations, 219—244, Amer. Math. Soc. Transl. Ser. 2, 232, Amer. Math. Soc., Providence, RI, 2014
  • W. Zajączkowski, Long time existence of regular solutions to non-homogeneous Navier-Stokes equations. Discrete Contin. Dyn. Syst. Ser. S 6 (2013), no. 5, 1427—1455 (link)
  • G. Seregin, V.A. Šverák, Rescalings at possible singularities of Navier-Stokes equations in half-space. Algebra i Analiz 25 (2013), no. 5, 146—172; reprinted in St. Petersburg Math. J. 25 (2014), no. 5, 815—833 (link)

2014

  • R. Farwig, On regularity of weak solutions to the instationary Navier-Stokes system: a review on recent results. Ann. Univ. Ferrara Sez. VII Sci. Mat. 60 (2014), no. 1, 91—122 (link)
  • M.-H. Giga, Y. Giga, P. Rybka, A comparison principle for singular diffusion equations with spatially inhomogeneous driving force for graphs. Arch. Ration. Mech. Anal. 211 (2014), no. 2, 419—453 (link)
  • C. Komo, Necessary and sufficient conditions for local strong solvability of the Navier-Stokes equations in exterior domains. J. Evol. Equ. 14 (2014), no. 3, 713—725 (link)
  • C. Komo, Optimal initial value conditions for the existence of strong solutions of the Boussinesq equations. Ann. Univ. Ferrara Sez. VII Sci. Mat. 60 (2014), no. 2, 377—396 (link)
  • T. Asai, Y. Giga, On self-similar solutions to the surface diffusion flow equations with contact angle boundary conditions. Interfaces Free Bound. 16 (2014), no. 4, 539—573 (link)
  • R. Farwig, Y. Giga, P.-Y. Hsu, Initial values for the Navier-Stokes equations in spaces with weights in time. TU Darmstadt Preprints, no. 2691, (2014) (pdf)
  • M.-H. Giga, Y. Giga, N. Požár, Periodic total variation flow of non-divergence type in $\mathbb{R}^n$. J. Math. Pures Appl. (9) 102 (2014), no. 1, 203—233 (link)

2015

  • C. Komo, Influence of surface roughness to solutions of the Boussinesq equations with Robin boundary condition. Rev. Mat. Complut. 28 (2015), no. 1, 123—151 (link)
  • Y. Giga, N. Hamamuki, A. Nakayasu, Eikonal equations in metric spaces. Trans. Amer. Math. Soc. 367 (2015), no. 1, 49—66. (link)
  • E. Zadrzyńska, W. Zajączkowski, Stability of two-dimensional Navier-Stokes motions in the periodic case. J. Math. Anal. Appl. 423 (2015), no. 2, 956—974 (link)
  • I. Denisova, On energy inequality for the problem on the evolution of two fluids of different types without surface tension. J. Math. Fluid Mech. 17 (2015), no. 1, 183—198 (link)
  • R. Farwig, T. Nakatsuka, Y. Taniuchi, Existence of solutions on the whole time axis to the Navier-Stokes equations with precompact range in $L^3$. Arch. Math. (Basel) 104 (2015), no. 6, 539—550 (link)
  • A. Kubica, P. Rybka, Fine singularity analysis of solutions to the Laplace equation Math. Methods Appl. Sci. 38 (2015), no. 9, 1734—1745. (link)
  • C. Komo, Uniqueness criteria and strong solutions of the Boussinesq equations in completely general domains. Z. Anal. Anwend. 34 (2015), no. 2, 147—164 (link)
  • G. Seregin, Liouville theorem for 2D Navier-Stokes equations in a half space. J. Math. Sci. (N.Y.) 210 (2015), no. 6, 849—856. (link)
  • T. Ohtsuka, T.-Y. R. Tsai, Y. Giga, A level set approach reflecting sheet structure with single auxiliary function for evolving spirals on crystal surfaces. J. Sci. Comput. 62 (2015), no. 3, 831—874 (link)
  • C. Komo, Strong solutions of the Boussinesq system in exterior domains. Analysis (Berlin) 35 (2015), no. 3, 161—175 (link)
  • E. Zadrzyńska, W. Zajączkowski, Stability of two-dimensional heat-conducting incompressible motions in a cylinder. Nonlinear Anal. 125 (2015), 113—127 (link)
  • S.A. Avdonin, A.S. Mikhaylov, V.S. Mikhaylov, On some applications of the Boundary Control method to spectral estimation and inverse problems., Nanosystems: Physics, Chemistry, Mathematics 6 (2015), 63—78 (link)

2016

  • R. Farwig, V. Rosteck, Resolvent estimates of the Stokes system with Navier boundary conditions in general unbounded domains. Adv. Differential Equations 21 (2016), no. 5-6, 401—428 (link)
  • R. Farwig, Y. Giga, Well-chosen Weak Solutions of the Instationary Navier-Stokes System and Their Uniqueness. TU Darmstadt Preprints, no. 2707, (2016) (pdf)
  • R. Farwig, Y. Giga, P.-Y. Hsu, The Navier-Stokes equations with initial values in Besov spaces of type $B^{-1+3/q}_{q,\infty}$. TU Darmstadt Preprints, no. 2709, (2016) (pdf)
  • Y. Giga, H. Mitake, H.V. Tran, On asymptotic speed of solutions to level-set mean curvature flow equations with driving and source terms. SIAM J. Math. Anal., 48 (2016), 3515—3546 (link)
  • Y. Giga, N. Pozar, A level set crystalline mean curvature flow of surfaces. Adv. Differential Equations, 21 (2016), 631—698. (link)
  • A. Kubica, P. Rybka, K. Ryszewska, Weak solutions of fractional differential equations in non cylindrical domains. Nonlinear Anal. Real World Appl., 36 (2017), 254—182 (link)
  • B. Nowakowski, W. Zajączkowski, Stability of two-dimensional magnetohydrodynamic motions in the periodic case. Math. Methods Appl. Sci. 39 (2016), no. 1, 44—61 (link)
  • W. Zajączkowski, Stability of two-dimensional solutions to the Navier-Stokes equations in cylindrical domains under Navier boundary conditions. J. Math. Anal. Appl. 444 (2016), no. 1, 275—297 (link)
  • B. Nowakowski, W. Zajączkowski, On global regular solutions to magnetohydrodynamics in axi-symmetric domains. Z. Angew. Math. Phys. 67 (2016), no. 6, Art. 142, 22 pp. (link)
  • R. Farwig, Y. Giga, P.-Y. Hsu, On the continuity of the solutions to the Navier-Stokes equations with initial data in critical Besov spaces. TU Darmstadt Preprints, no. 2710, (2016) (pdf)
  • R. Farwig, Y. Giga, P.-Y. Hsu, Initial values for the Navier-Stokes equations in spaces with weights in time. Funkcial. Ekvac. 59 (2016), no. 2, 199—216 (link)
  • A. Nakayasu, P. Rybka, Viscosity solutions to one-dimensional singular parabolic problems with BV data. Submitted
  • R. Farwig, H. Kozono, D. Wegmann, Decay of non-stationary Navier-Stokes flow with nonzero Dirichlet boundary data. Indiana Univ. Math. J., online first (link)
  • A. Kubica, P. Rybka, Fine singularity analysis of solutions to the Laplace equation: Berg's effect. Math. Methods Appl. Sci. 39 (2016), no. 5, 1069—1075 (link)
  • M. Matusik, P. Rybka, Oscillating facets. Port. Math. 73 (2016), no. 1, 1—40 (link)
  • J. Burczak, W. Zajączkowski, Quantitative robustness of regularity for 3D Navier–Stokes system in Hα-spaces. Nonlinear Anal. Real World Appl. 31 (2016), 513—532 (link)
  • R. Farwig, H. Kozono, D. Wegmann, Existence of strong solutions and decay of turbulent solutions of Navier-Stokes flow with nonzero Dirichlet boundary data. Submitted
  • J. Gawinecki, W. Zajączkowski, On regular solutions to two-dimensional thermoviscoelasticity. Appl. Math. (Warsaw) 43 (2016), no. 2, 207—233 (link)
  • J. Gawinecki, W. Zajączkowski, Global regular solutions to two-dimensional thermoviscoelasticity. Commun. Pure Appl. Anal. 15 (2016), 1009—1028 (link)
  • V.A. Solonnikov, On the solvability of free boundary value problem for viscous compressible fluids in an infinite time interval., Springer Proceedings in Mathematics and Statistics, Mathematical fluid dynamics, present and future, 2016, Vol. 183, pp. 287—315 (link)
  • T. Shilkin, N. Filonov, On the local boundedness of weak solutions to elliptic equations with divergence-free drifts. TU Darmstadt, Preprint no. 2714 (link)
  • A. Mikhaylov, J. Rencławowicz, W.M. Zajączkowski, On global regular solutions to the mhd equations in smooth toroidal domain, Appl. Math. (Warsaw), to appear.
  • S.I, Repin, On variational representations of the constant in the inf sup condition for the Stokes problem. Zapiski Nauchn. Semin. POMI, v. 444 (2016), pp. 110—123 (link)
  • G.A. Seregin, Liouville type theorem for stationary Navier–Stokes equations. Nonlinearity 29 (2016), 2191—2195 (link)
  • G. Seregin, V. Šverák, On global weak solutions to the Cauchy problem for the Navier-Stokes equations with large L3-initial data,, Nonlinear Anal. 154 (2017), 269—296 (link)
  • G. Seregin, Caffarelli-Kohn-Nirenberg and the Navier-Stokes problem., Notices of the American Mathematical Society, 2016, Vol. 63, no. 2 pp. 130—131 (link)
  • G. Seregin, Remark on Wolf's condition for boundary regularity of Navier-Stokes equations., Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 444 (2016), 124—132 (link)
  • V.A. Solonnikov, Proof of Schauder estimates for parabolic initial-boundary value model problems via O. A. Ladyzhenskaya's Fourier multipliers theorem. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 444 (2016), 133—156 (link)