With the formulation of the gauge group as a Banach-Lie group of suitable Sobolev type, the Cauchy problem for the Yang-Mills equation in physical space-time reduces rigorously to the case of the temporal gauge. In this gauge there exist spatially global strong solutions for given data for field and potential that are L(2) together with one or two derivatives (respectively). Regarding global ex...

In this paper, we study the viscous Boussinesq equation in whole space $\mathbb{R}^n$, which describes propagation of small amplitude and long waves on surface water with effects. Concerning linearized Cauchy problem, some qualitative properties solutions including $L^m-L^q$ estimates $1\leqslant m\leqslant q\leqslant \infty$, inviscid limits asymptotic profiles solution respect to viscosity ar...

If A is a Lipschitz function, i.e., || A |L < °°, then %A makes a very significant example of non-convolution type singular integral operators. The problem of L -boundedness of the Cauchy transform was raised and solved when || A |L is small by A. P. Calderόn in relation to the Dirichlet problem on Lipschitz domains [Call, Cal2]. Since then, it has been a central problem in the theory of singul...

We examine the evidence for the widespread belief that heavy tail distributions enhance the search for minima on multimodal objective functions. We analyze isotropic and anisotropic heavy-tail Cauchy distributions and investigate the probability to sample a better solution, depending on the step length and the dimensionality of the search space. The probability decreases fast with increasing st...

Abstract This article considers the Cauchy problem for compressible Euler system in R {\bf{R}} with damping, which coefficient depends on space variable. Assuming initial density has a small perturbation around constant state and both velocity field are compact supported, finite-time blow-up result w...

We focus on a Cauchy problem for impulsive integrodifferential equations involving nonlocal initial conditions, where the linear part is a generator of a solution operator on a complex Banach space. A suitable mild solution for the Cauchy problem is introduced. The existence and uniqueness of mild solutions for the Cauchy problem, under various criterions, are proved. In the last part of the pa...