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Weak Solutions of Ideal MHD Which Do Not Conserve Magnetic Helicity
Annals of PDE, 2019We construct weak solutions to the ideal magneto-hydrodynamic (MHD) equations which have finite total energy, and whose magnetic helicity is not a constant function of time.
Rajendra Beekie, T. Buckmaster, V. Vicol
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Weak Solutions for Obstacle Problems with Weak Monotonicity
Studia Scientiarum Mathematicarum Hungarica, 2021This paper is concerned with the existence of weak solutions for obstacle problems. By means of the Young measure theory and a theorem of Kinderlehrer and Stampacchia, we obtain the needed result.
Farah Balaadich, Elhoussine Azroul
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WEAK SOLUTIONS FOR WEAK SINGULARITIES
International Journal of Modern Physics A, 2002We revisit the problem of the development of singularities in the gravitational collapse of an inhomogeneous dust sphere. As shown by Yodzis et al1, naked singularities may occur at finite radius where shells of dust cross one another. These singularities are gravitationally weak 2, and it has been claimed that at these singularities, the metric may ...
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Non-uniqueness and h-Principle for Hölder-Continuous Weak Solutions of the Euler Equations
, 2016In this paper we address the Cauchy problem for the incompressible Euler equations in the periodic setting. We prove that the set of Hölder $${1/5 - \varepsilon}$$1/5-ε wild initial data is dense in $${L^{2}}$$L2, where we call an initial datum wild if ...
S. Daneri, L. Székelyhidi
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2021
Weak solutions, of variational inequality type, are introduced. Their defining properties can be equivalently expressed in terms of quadrature identities for subharmonic functions, or in terms of partial balayage. Some versions of inverse balayage are also discussed, this needed as a preparatory step for constructing more general Laplacian evolutions ...
Björn Gustafsson, Yu-Lin Lin
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Weak solutions, of variational inequality type, are introduced. Their defining properties can be equivalently expressed in terms of quadrature identities for subharmonic functions, or in terms of partial balayage. Some versions of inverse balayage are also discussed, this needed as a preparatory step for constructing more general Laplacian evolutions ...
Björn Gustafsson, Yu-Lin Lin
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Weak Solutions for Semi-Martingales
Canadian Journal of Mathematics, 1981The fundamental theorem of this paper is stated in Section 8. In this theorem, the stochastic differential equation dX = a(X)dZ is studied when Z is a *-dominated (cf. [15]) Banach space valued process and a is a predictable functional which is continuous for the uniform norm.For such an equation, the existence of a “weak solution” is stated; actually,
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Global Existence of Finite Energy Weak Solutions of Quantum Navier–Stokes Equations
, 2016In this paper we consider the Quantum Navier–Stokes system both in two and in three space dimensions and prove the global existence of finite energy weak solutions for large initial data.
P. Antonelli, Stefano Spirito
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Uniqueness of weak solutions to a Keller-Segel-Navier-Stokes system
Applied Mathematics Letters, 2021Miaochao Chen, Sheng-Sen Lu, Qilin Liu
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