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Qianzhu Tian - One of the best experts on this subject based on the ideXlab platform.

  • The nonlinear Boundary layer to the Boltzmann equation for cutoff soft potential with Physical Boundary Condition
    Nonlinear Analysis: Real World Applications, 2011
    Co-Authors: Jie Sun, Qianzhu Tian
    Abstract:

    Abstract We consider the nonlinear Boundary layer to the Boltzmann equation for cutoff soft potential with Physical Boundary Condition, i.e., the Dirichlet Boundary Condition with weak diffuse effect. Under the assumption that the distribution function of gas particles tends to a global Maxwellian in the far field, we will show the Boundary layer exist if the Boundary data satisfy the solvability Condition. Moreover, the codimensions of the Boundary data which satisfies the solvability Condition change with the Mach number of the far field Maxwellian like Chen et al. (2004)  [5] , Ukai et al. (2003)  [6] and Wang et al. (2007)  [7] .

Jie Sun - One of the best experts on this subject based on the ideXlab platform.

  • The nonlinear Boundary layer to the Boltzmann equation for cutoff soft potential with Physical Boundary Condition
    Nonlinear Analysis: Real World Applications, 2011
    Co-Authors: Jie Sun, Qianzhu Tian
    Abstract:

    Abstract We consider the nonlinear Boundary layer to the Boltzmann equation for cutoff soft potential with Physical Boundary Condition, i.e., the Dirichlet Boundary Condition with weak diffuse effect. Under the assumption that the distribution function of gas particles tends to a global Maxwellian in the far field, we will show the Boundary layer exist if the Boundary data satisfy the solvability Condition. Moreover, the codimensions of the Boundary data which satisfies the solvability Condition change with the Mach number of the far field Maxwellian like Chen et al. (2004)  [5] , Ukai et al. (2003)  [6] and Wang et al. (2007)  [7] .

Ouyang Zhimeng - One of the best experts on this subject based on the ideXlab platform.

  • The Landau equation with the specular reflection Boundary Condition
    'Springer Science and Business Media LLC', 2019
    Co-Authors: Guo Yan, Hyung Ju Hwang, Jang, Jin Woo, Ouyang Zhimeng
    Abstract:

    The existence and stability of the Landau equation (1936) in a general bounded domain with a Physical Boundary Condition is a long-outstanding open problem. This work proves the global stability of the Landau equation with the Coulombic potential in a general smooth bounded domain with the specular reflection Boundary Condition for initial perturbations of the Maxwellian equilibrium states. The highlight of this work also comes from the low-regularity assumptions made for the initial distribution. This work generalizes the recent global stability result for the Landau equation in a periodic box (KGH-2016). Our methods consist of the generalization of the wellposedness theory for the Fokker-Planck equation (HJV-2014, HJJ-2018) and the extension of the Boundary value problem to a whole space problem, as well as the use of a recent extension of De Giorgi-Nash-Moser theory for the kinetic Fokker-Planck equations (GIMV-2016) and the Morrey estimates (Polidoro-Ragusa-1998) to further control the velocity derivatives, which ensures the uniqueness. Our methods provide a new understanding of the grazing collisions in the Landau theory for an initial-Boundary value problem.Comment: 56 page

Zm Ouyang - One of the best experts on this subject based on the ideXlab platform.

  • The Landau Equation with the Specular Reflection Boundary Condition
    'Springer Fachmedien Wiesbaden GmbH', 2020
    Co-Authors: Guo Y, Hj Hwang, Jinwoo Jang, Zm Ouyang
    Abstract:

    The existence and stability of the Landau equation (1936) in a general bounded domain with a Physical Boundary Condition is a long-outstanding open problem. This work proves the global stability of the Landau equation with the Coulombic potential in a general smooth bounded domain with the specular reflection Boundary Condition for initial perturbations of the Maxwellian equilibrium states. The highlight of this work also comes from the low-regularity assumptions made for the initial distribution. This work generalizes the recent global stability result for the Landau equation in a periodic box (Kim et al. in Peking Math J, 2020). Our methods consist of the generalization of the wellposedness theory for the Fokker-Planck equation (Hwang et al. SIAM J Math Anal 50(2):2194-2232, 2018; Hwang et al. Arch Ration Mech Anal 214(1):183-233, 2014) and the extension of the Boundary value problem to a whole space problem, as well as the use of a recent extension of De Giorgi-Nash-Moser theory for the kinetic Fokker-Planck equations (Golse et al. Ann Sc Norm Super Pisa Cl Sci 19(1):253-295, 2019) and the Morrey estimates (Bramanti et al. J Math Anal Appl 200(2):332-354, 1996) to further control the velocity derivatives, which ensures the uniqueness. Our methods provide a new understanding of the grazing collisions in the Landau theory for an initial-Boundary value problem. © Springer-Verlag GmbH Germany, part of Springer Nature (2020

Rama Bhargava - One of the best experts on this subject based on the ideXlab platform.

  • numerical investigation of the effect of magnetic field on the onset of nanofluid convection
    Applied Thermal Engineering, 2016
    Co-Authors: Dhananjay Yadav, Junye Wang, Rama Bhargava
    Abstract:

    Abstract The present analysis aims at investigating the effect of a uniform vertical magnetic field on the onset of convection in an electrically conducting nanofluid layer with a new set of Physical Boundary Condition. It is assumed that the value of the temperature can be imposed on the boundaries, but the nanoparticle fraction adjusts together with effects of Brownian and thermophoresis so that the nanoparticle flux is zero on the boundaries. Using the Galerkin method, the critical Rayleigh number on the onset of convection and the corresponding wave number are obtained in terms of various parameters numerically. The numerical computations are presented for water-based nanofluids with Al2O3 and Cu nanoparticles. It is found that the volumetric fraction of nanoparticle, the Lewis number, the modified diffusivity and the density ratios have a destabilizing effect, while the magnetic field has stabilizing effect on the system. The zero flux nanoparticle Boundary Condition has more destabilizing effect than the constant nanoparticle Boundary Conditions for Al2O3–water nanofluid, while reverse for Cu–water nanofluid.