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The Liouville theorems for 3D stationary tropical climate model
Mathematical methods in the applied sciences, 2021In this paper, we will consider the Liouville theorems for the 3D stationary tropical climate model in whole space. In particular, we will prove that there is only the trivial solution for the stationary tropical climate model under some integrable ...
Huiting Ding, Fan Wu
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Liouville theorems for fractional and higher-order Hénon–Hardy systems on ℝn
Complex Variables and Elliptic Equations, 2020In this paper, we are concerned with the Hénon–Hardy type systems on : where , , or . We prove Liouville theorems (i.e. non-existence of nontrivial nonnegative solutions) for the above Hénon–Hardy systems. The arguments used in our proof is the method of
Shaolong Peng
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1998
Abstract This result has a long history. For diffeomorphisms of class C in ℝ Liouville established the result in 1850 [204] along the lines we discussed in the chapter on conformal geometry. The relaxation of the differentiability hypotheses and the local injectivity assumptions are significant steps since the aim is to describe the ...
Tadeusz Iwaniec, Gaven Martin
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Abstract This result has a long history. For diffeomorphisms of class C in ℝ Liouville established the result in 1850 [204] along the lines we discussed in the chapter on conformal geometry. The relaxation of the differentiability hypotheses and the local injectivity assumptions are significant steps since the aim is to describe the ...
Tadeusz Iwaniec, Gaven Martin
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On Local Type I Singularities of the Navier–Stokes Equations and Liouville Theorems
Journal of Mathematical Fluid Mechanics, 2018We prove that suitable weak solutions of the Navier–Stokes equations exhibit Type I singularities if and only if there exists a non-trivial mild bounded ancient solution satisfying a Type I decay condition.
D. Albritton, T. Barker
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A Liouville theorem on a manifold
Russian Mathematical Surveys, 1982Translation from Usp. Mat. Nauk 37, No.3(225), 181-182 (Russian) (1982; Zbl 0509.53035).
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2014
A complex number α is said to be an algebraic number if there is a non-zero polynomial \(f(x) \in \mathbb{Q}[x]\) such that f(α) = 0. Given an algebraic number α, there exists a unique irreducible monic polynomial \(P(x) \in \mathbb{Q}[x]\) such that P(α) = 0. This is called the minimal polynomial of α.
Purusottam Rath, M. Ram Murty
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A complex number α is said to be an algebraic number if there is a non-zero polynomial \(f(x) \in \mathbb{Q}[x]\) such that f(α) = 0. Given an algebraic number α, there exists a unique irreducible monic polynomial \(P(x) \in \mathbb{Q}[x]\) such that P(α) = 0. This is called the minimal polynomial of α.
Purusottam Rath, M. Ram Murty
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Liouville theorems for scaling invariant superlinear parabolic problems with gradient structure
, 2014We provide a simple method for obtaining new Liouville theorems for scaling invariant superlinear parabolic problems with gradient structure. To illustrate the method we prove Liouville theorems (guaranteeing nonexistence of positive classical solutions)
P. Quittner
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