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Creators/Authors contains: "Kukavica, Igor"

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  1. ; ; (, Journal of Mathematical Fluid Mechanics)
    Abstract We examine a micro-scale model of superfluidity derived by Pitaevskii (Sov. Phys. JETP 8:282-287, 1959) which describes the interacting dynamics between superfluid He-4 and its normal fluid phase. This system consists of the nonlinear Schrödinger equation and the incompressible, inhomogeneous Navier-Stokes equations, coupled to each other via a bidirectional nonlinear relaxation mechanism. The coupling permits mass/momentum/energy transfer between the phases, and accounts for the conversion of superfluid into normal fluid. We prove the existence of global weak solutions in$${\mathbb {T}}^3$$ T 3 for a power-type nonlinearity, beginning from small initial data. The main challenge is to control the inter-phase mass transfer in order to ensure the strict positivity of the normal fluid density, while obtaining time-independent a priori estimates. 
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  2. ; ; (, Nonlinearity)
    Abstract We investigate a micro-scale model of superfluidity derived by Pitaevskii (1959Sov. Phys. JETP8282–7) to describe the interacting dynamics between the superfluid and normal fluid phases of Helium-4. The model involves the nonlinear Schrödinger equation (NLS) and the Navier–Stokes equations, coupled to each other via a bidirectional nonlinear relaxation mechanism. Depending on the nature of the nonlinearity in the NLS, we prove global/almost global existence of solutions to this system in T 2 —strong in wavefunction and velocity, and weak in density. 
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  3. ; (, Journal of Differential Equations)
    Full Text Available 
  4. ; (, Journal of Dynamics and Differential Equations)
    Full Text Available 
  5. ; (, Journal of Differential Equations)
    Full Text Available 
  6. ; ; (, Discrete and Continuous Dynamical Systems)
    Full Text Available 
  7. ; ; (, Archive for Rational Mechanics and Analysis)
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  8. ; ; (, Journal of Differential Equations)
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  9. ; ; (, Pure and applied functional analysis)
    Accepted Manuscript Full Text Available
  10. ; ; (, Stochastics and Partial Differential Equations: Analysis and Computations)
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