7,081 research outputs found
Regularizing effect and local existence for non-cutoff Boltzmann equation
The Boltzmann equation without Grad's angular cutoff assumption is believed
to have regularizing effect on the solution because of the non-integrable
angular singularity of the cross-section. However, even though so far this has
been justified satisfactorily for the spatially homogeneous Boltzmann equation,
it is still basically unsolved for the spatially inhomogeneous Boltzmann
equation. In this paper, by sharpening the coercivity and upper bound estimates
for the collision operator, establishing the hypo-ellipticity of the Boltzmann
operator based on a generalized version of the uncertainty principle, and
analyzing the commutators between the collision operator and some weighted
pseudo differential operators, we prove the regularizing effect in all (time,
space and velocity) variables on solutions when some mild regularity is imposed
on these solutions. For completeness, we also show that when the initial data
has this mild regularity and Maxwellian type decay in velocity variable, there
exists a unique local solution with the same regularity, so that this solution
enjoys the regularity for positive time
The Boltzmann equation without angular cutoff in the whole space: II, Global existence for hard potential
As a continuation of our series works on the Boltzmann equation without
angular cutoff assumption, in this part, the global existence of solution to
the Cauchy problem in the whole space is proved in some suitable weighted
Sobolev spaces for hard potential when the solution is a small perturbation of
a global equilibrium
Global existence and full regularity of the Boltzmann equation without angular cutoff
We prove the global existence and uniqueness of classical solutions around an
equilibrium to the Boltzmann equation without angular cutoff in some Sobolev
spaces. In addition, the solutions thus obtained are shown to be non-negative
and in all variables for any positive time. In this paper, we study
the Maxwellian molecule type collision operator with mild singularity. One of
the key observations is the introduction of a new important norm related to the
singular behavior of the cross section in the collision operator. This norm
captures the essential properties of the singularity and yields precisely the
dissipation of the linearized collision operator through the celebrated
H-theorem
Direct and trans-generational effects of male and female gut microbiota in Drosophila melanogaster
Funding This study was supported by the National Council for Scientific and Technological Development (CNPq). Acknowledgement We acknowledge Stuart Wigby, Adam Wong and Phil Taylor for discussion and support during the experiment.Peer reviewedPublisher PD
Well-posedness of the Viscous Boussinesq System in Besov Spaces of Negative Order Near Index
This paper is concerned with well-posedness of the Boussinesq system. We
prove that the () dimensional Boussinesq system is well-psoed for
small initial data () either in
or in
if
, and , where
(, , )
is the logarithmically modified Besov space to the standard Besov space
. We also prove that this system is well-posed for small initial
data in
.Comment: 18 page
Analysis of Magnetization Reversal Process of Nd-Fe-B Sintered Magnets by Magnetic Domain Observation Using Kerr Microscope
We used a Kerr microscope, image processing, and photo editing to clarify magnetization reversal and its propagation in a sintered Nd-Fe-B magnet. Magnetic domain change was observed when a dc field from +20 to 20 kOe was applied to a sintered Nd-Fe-B magnet. Simultaneous magnetization reversal in several grains along the easy axis direction and its propagation to neighboring grains occurred. This indicates that the nucleation field in a grain and magnetic interaction between grains are important controlling factors of the coercivity of sintered Nd-Fe-B magnets
Skin-Derived TSLP Triggers Progression from Epidermal-Barrier Defects to Asthma
A skin-derived cytokine with high systemic availability provides a mechanistic explanation for atopic march and highlights a potential therapeutic target for preventing the development of asthma among people with atopic dermatitis
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